diff --git a/python/src/com/jetbrains/python/PyBundle.properties b/python/src/com/jetbrains/python/PyBundle.properties
index fbd9d64acd91..2e44a53bdadf 100644
--- a/python/src/com/jetbrains/python/PyBundle.properties
+++ b/python/src/com/jetbrains/python/PyBundle.properties
@@ -604,6 +604,7 @@ refactoring.extract.method.error.local.variable.modifications.and.returns=Cannot
 refactoring.extract.method.error.empty.fragment=Cannot perform refactoring from empty code fragment
 refactoring.extract.method.error.undetermined.execution.flow=Cannot determine execution flow for the code fragment
 refactoring.extract.method.error.yield=Cannot perform refactoring with 'yield' statement inside code block
+refactoring.extract.method.error.class.level=Cannot perform refactoring at class level
 
 
 # extract superclass
diff --git a/python/src/com/jetbrains/python/refactoring/extractmethod/PyExtractMethodHandler.java b/python/src/com/jetbrains/python/refactoring/extractmethod/PyExtractMethodHandler.java
index 708a27700fb6..ac92a559d076 100644
--- a/python/src/com/jetbrains/python/refactoring/extractmethod/PyExtractMethodHandler.java
+++ b/python/src/com/jetbrains/python/refactoring/extractmethod/PyExtractMethodHandler.java
@@ -31,6 +31,7 @@ import com.jetbrains.python.PyBundle;
 import com.jetbrains.python.codeInsight.codeFragment.PyCodeFragment;
 import com.jetbrains.python.codeInsight.codeFragment.PyCodeFragmentUtil;
 import com.jetbrains.python.codeInsight.controlflow.ScopeOwner;
+import com.jetbrains.python.psi.PyClass;
 import com.jetbrains.python.psi.PyElement;
 import com.jetbrains.python.psi.impl.PyPsiUtils;
 import com.jetbrains.python.refactoring.PyRefactoringUtil;
@@ -82,6 +83,11 @@ public class PyExtractMethodHandler implements RefactoringActionHandler {
                                           RefactoringBundle.message("extract.method.title"), "refactoring.extractMethod");
       return;
     }
+    if (rangeBelongsToSameClassBody(element1, element2)) {
+      CommonRefactoringUtil.showErrorHint(project, editor, PyBundle.message("refactoring.extract.method.error.class.level"),
+                                          RefactoringBundle.message("extract.method.title"), "refactoring.extractMethod");
+      return;
+    }
 
     final Couple<PsiElement> statements = getStatementsRange(element1, element2);
     if (statements != null) {
@@ -126,6 +132,12 @@ public class PyExtractMethodHandler implements RefactoringActionHandler {
                                         RefactoringBundle.message("extract.method.title"), "refactoring.extractMethod");
   }
 
+  private static boolean rangeBelongsToSameClassBody(@NotNull PsiElement element1, @NotNull PsiElement element2) {
+    final PyClass firstScopeOwner = PsiTreeUtil.getParentOfType(element1, PyClass.class, false, ScopeOwner.class);
+    final PyClass secondScopeOwner = PsiTreeUtil.getParentOfType(element2, PyClass.class, false, ScopeOwner.class);
+    return firstScopeOwner != null && firstScopeOwner == secondScopeOwner;
+  }
+
   @Nullable
   private static Couple<PsiElement> getStatementsRange(final PsiElement element1, final PsiElement element2) {
     final PsiElement parent = PsiTreeUtil.findCommonParent(element1, element2);
diff --git a/python/testData/refactoring/extractmethod/ClassContext.after.py b/python/testData/refactoring/extractmethod/ClassContext.after.py
deleted file mode 100644
index d8d43cddfcb9..000000000000
--- a/python/testData/refactoring/extractmethod/ClassContext.after.py
+++ /dev/null
@@ -1,5 +0,0 @@
-class PyCharm:
-    def bar():
-        print("Hello Pycharm!")
-
-    bar()
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/ClassContext.before.py b/python/testData/refactoring/extractmethod/ClassContext.before.py
deleted file mode 100644
index b33d3dea282a..000000000000
--- a/python/testData/refactoring/extractmethod/ClassContext.before.py
+++ /dev/null
@@ -1,2 +0,0 @@
-class PyCharm:
-    <selection>print("Hello Pycharm!")</selection>
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/Comment2.after.py b/python/testData/refactoring/extractmethod/Comment2.after.py
deleted file mode 100644
index c5cc3a7ff224..000000000000
--- a/python/testData/refactoring/extractmethod/Comment2.after.py
+++ /dev/null
@@ -1,8 +0,0 @@
-class Foo():
-    def baz():
-        tmp = "!"  # try to extract this assignment, either with or without this comment
-
-    baz()
-
-    def bar(self):
-        pass
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/Comment2.before.py b/python/testData/refactoring/extractmethod/Comment2.before.py
deleted file mode 100644
index 23ba13de61f7..000000000000
--- a/python/testData/refactoring/extractmethod/Comment2.before.py
+++ /dev/null
@@ -1,5 +0,0 @@
-class Foo():
-    <selection>tmp = "!" #try to extract this assignment, either with or without this comment</selection>
-
-    def bar(self):
-        pass
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/CommentIncluded.after.py b/python/testData/refactoring/extractmethod/CommentIncluded.after.py
new file mode 100644
index 000000000000..6bfc159140a0
--- /dev/null
+++ b/python/testData/refactoring/extractmethod/CommentIncluded.after.py
@@ -0,0 +1,8 @@
+def baz():
+    tmp = "!"  # try to extract this assignment, either with or without this comment
+
+
+baz()
+
+def bar(self):
+    pass
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/CommentIncluded.before.py b/python/testData/refactoring/extractmethod/CommentIncluded.before.py
new file mode 100644
index 000000000000..0b5dcef55ec4
--- /dev/null
+++ b/python/testData/refactoring/extractmethod/CommentIncluded.before.py
@@ -0,0 +1,4 @@
+<selection>tmp = "!" #try to extract this assignment, either with or without this comment</selection>
+
+def bar(self):
+    pass
\ No newline at end of file
diff --git a/python/testData/refactoring/extractmethod/NameCollisionClass.before.py b/python/testData/refactoring/extractmethod/NameCollisionClass.before.py
deleted file mode 100644
index 5aa02294eab8..000000000000
--- a/python/testData/refactoring/extractmethod/NameCollisionClass.before.py
+++ /dev/null
@@ -1,5 +0,0 @@
-class A:
-    def hello():
-      pass
-
-    <selection>print("Hello")</selection>
diff --git a/python/testData/refactoring/extractmethod/ProhibitedAtClassLevel.before.py b/python/testData/refactoring/extractmethod/ProhibitedAtClassLevel.before.py
new file mode 100644
index 000000000000..0630f2dfcfaa
--- /dev/null
+++ b/python/testData/refactoring/extractmethod/ProhibitedAtClassLevel.before.py
@@ -0,0 +1,2 @@
+class C():
+    <selection>some_class_field = 1</selection>
\ No newline at end of file
diff --git a/python/testSrc/com/jetbrains/python/refactoring/PyExtractMethodTest.java b/python/testSrc/com/jetbrains/python/refactoring/PyExtractMethodTest.java
index bfa342969b5f..1ebebf000efe 100644
--- a/python/testSrc/com/jetbrains/python/refactoring/PyExtractMethodTest.java
+++ b/python/testSrc/com/jetbrains/python/refactoring/PyExtractMethodTest.java
@@ -101,10 +101,6 @@ public class PyExtractMethodTest extends LightMarkedTestCase {
     doTest("bar");
   }
 
-  public void testNameCollisionClass() {
-    doFail("hello", "Method name clashes with already existing name");
-  }
-
   public void testNameCollisionFile() {
     doFail("hello", "Method name clashes with already existing name");
   }
@@ -149,10 +145,6 @@ public class PyExtractMethodTest extends LightMarkedTestCase {
     doTest("bar");
   }
 
-  public void testClassContext() {
-    doTest("bar");
-  }
-
   public void testConditionalReturn() {
     doFail("bar", "Cannot perform refactoring when execution flow is interrupted");
   }
@@ -161,7 +153,7 @@ public class PyExtractMethodTest extends LightMarkedTestCase {
     doTest("bar");
   }
 
-  public void testComment2() {
+  public void testCommentIncluded() {
     doTest("baz");
   }
 
@@ -281,4 +273,9 @@ public class PyExtractMethodTest extends LightMarkedTestCase {
   public void testRedundantGlobalInTopLevelFunction() {
     doTest("foo");
   }
+
+  // PY-6620
+  public void testProhibitedAtClassLevel() {
+    doFail("foo", "Cannot perform refactoring at class level");
+  }
 }