diff --git a/AUTHORS b/AUTHORS
index 00ced49f0..d7be48075 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -166,6 +166,7 @@ Miro Hrončok
 Nathaniel Waisbrot
 Ned Batchelder
 Neven Mundar
+Nicholas Devenish
 Niclas Olofsson
 Nicolas Delaby
 Oleg Pidsadnyi
diff --git a/changelog/4327.bugfix.rst b/changelog/4327.bugfix.rst
new file mode 100644
index 000000000..72223af4e
--- /dev/null
+++ b/changelog/4327.bugfix.rst
@@ -0,0 +1 @@
+``approx`` again works with more generic containers, more precisely instances of ``Iterable`` and ``Sized`` instead of more restrictive ``Sequence``.
diff --git a/src/_pytest/compat.py b/src/_pytest/compat.py
index 6008b8b40..ff027f308 100644
--- a/src/_pytest/compat.py
+++ b/src/_pytest/compat.py
@@ -45,11 +45,11 @@ MODULE_NOT_FOUND_ERROR = "ModuleNotFoundError" if PY36 else "ImportError"
 
 if _PY3:
     from collections.abc import MutableMapping as MappingMixin
-    from collections.abc import Mapping, Sequence
+    from collections.abc import Iterable, Mapping, Sequence, Sized
 else:
     # those raise DeprecationWarnings in Python >=3.7
     from collections import MutableMapping as MappingMixin  # noqa
-    from collections import Mapping, Sequence  # noqa
+    from collections import Iterable, Mapping, Sequence, Sized  # noqa
 
 
 if sys.version_info >= (3, 4):
diff --git a/src/_pytest/python_api.py b/src/_pytest/python_api.py
index 92674589f..4e4740192 100644
--- a/src/_pytest/python_api.py
+++ b/src/_pytest/python_api.py
@@ -15,8 +15,9 @@ from six.moves import zip
 import _pytest._code
 from _pytest import deprecated
 from _pytest.compat import isclass
+from _pytest.compat import Iterable
 from _pytest.compat import Mapping
-from _pytest.compat import Sequence
+from _pytest.compat import Sized
 from _pytest.compat import STRING_TYPES
 from _pytest.outcomes import fail
 
@@ -186,7 +187,7 @@ class ApproxMapping(ApproxBase):
                 raise _non_numeric_type_error(self.expected, at="key={!r}".format(key))
 
 
-class ApproxSequence(ApproxBase):
+class ApproxSequencelike(ApproxBase):
     """
     Perform approximate comparisons where the expected value is a sequence of
     numbers.
@@ -522,10 +523,14 @@ def approx(expected, rel=None, abs=None, nan_ok=False):
         cls = ApproxScalar
     elif isinstance(expected, Mapping):
         cls = ApproxMapping
-    elif isinstance(expected, Sequence) and not isinstance(expected, STRING_TYPES):
-        cls = ApproxSequence
     elif _is_numpy_array(expected):
         cls = ApproxNumpy
+    elif (
+        isinstance(expected, Iterable)
+        and isinstance(expected, Sized)
+        and not isinstance(expected, STRING_TYPES)
+    ):
+        cls = ApproxSequencelike
     else:
         raise _non_numeric_type_error(expected, at=None)
 
diff --git a/testing/python/approx.py b/testing/python/approx.py
index 96433d52b..26e6a4ab2 100644
--- a/testing/python/approx.py
+++ b/testing/python/approx.py
@@ -496,3 +496,14 @@ class TestApprox(object):
         assert actual != approx(expected, rel=5e-8, abs=0)
         assert approx(expected, rel=5e-7, abs=0) == actual
         assert approx(expected, rel=5e-8, abs=0) != actual
+
+    def test_generic_sized_iterable_object(self):
+        class MySizedIterable(object):
+            def __iter__(self):
+                return iter([1, 2, 3, 4])
+
+            def __len__(self):
+                return 4
+
+        expected = MySizedIterable()
+        assert [1, 2, 3, 4] == approx(expected)