diff --git a/src/_pytest/python_api.py b/src/_pytest/python_api.py
index 10762ee7b..576f6109d 100644
--- a/src/_pytest/python_api.py
+++ b/src/_pytest/python_api.py
@@ -459,8 +459,8 @@ class ApproxScalar(ApproxBase):
         result: bool = abs(self.expected - actual) <= self.tolerance
         return result
 
-    # Ignore type because of https://github.com/python/mypy/issues/4266.
-    __hash__ = None  # type: ignore
+    def __hash__(self):
+        return hash(self.expected)
 
     @property
     def tolerance(self):
diff --git a/testing/python/approx.py b/testing/python/approx.py
index 6acb466ff..6fff32c85 100644
--- a/testing/python/approx.py
+++ b/testing/python/approx.py
@@ -346,6 +346,10 @@ class TestApprox:
         assert 10 != approx(1, rel=1e-6, abs=1e-12)
         assert not (10 == approx(1, rel=1e-6, abs=1e-12))
 
+    def test_hash(self):
+        assert {1} == {approx(1, rel=1e-6, abs=1e-12)}
+        assert {1+1e-5} != {approx(1, rel=1e-6, abs=1e-12)}
+
     def test_exactly_equal(self):
         examples = [
             (2.0, 2.0),