diff --git a/changelog/3695.bugfix.rst b/changelog/3695.bugfix.rst
new file mode 100644
index 00000000000..42d07336b51
--- /dev/null
+++ b/changelog/3695.bugfix.rst
@@ -0,0 +1,2 @@
+Fix ``ApproxNumpy`` initialisation argument mixup, ``abs`` and ``rel`` tolerances were flipped causing strange comparsion results.
+Add tests to check ``abs`` and ``rel`` tolerances for ``np.array`` and test for expecting ``nan`` with ``np.array()``
diff --git a/src/_pytest/python_api.py b/src/_pytest/python_api.py
index d88d1c88bb9..5331d8a84a3 100644
--- a/src/_pytest/python_api.py
+++ b/src/_pytest/python_api.py
@@ -211,7 +211,7 @@ def __eq__(self, actual):
         the pre-specified tolerance.
         """
         if _is_numpy_array(actual):
-            return ApproxNumpy(actual, self.abs, self.rel, self.nan_ok) == self.expected
+            return all(a == self for a in actual.flat)
 
         # Short-circuit exact equality.
         if actual == self.expected:
diff --git a/testing/python/approx.py b/testing/python/approx.py
index 39f10a82116..0509fa67238 100644
--- a/testing/python/approx.py
+++ b/testing/python/approx.py
@@ -342,6 +342,68 @@ def test_numpy_array(self):
         assert actual == approx(list(expected), rel=5e-7, abs=0)
         assert actual != approx(list(expected), rel=5e-8, abs=0)
 
+    def test_numpy_tolerance_args(self):
+        """
+        Check that numpy rel/abs args are handled correctly
+        for comparison against an np.array
+        Check both sides of the operator, hopefully it doesn't impact things.
+        Test all permutations of where the approx and np.array() can show up
+        """
+        np = pytest.importorskip("numpy")
+        expected = 100.
+        actual = 99.
+        abs_diff = expected - actual
+        rel_diff = (expected - actual) / expected
+
+        tests = [
+            (eq, abs_diff, 0),
+            (eq, 0, rel_diff),
+            (ne, 0, rel_diff / 2.),  # rel diff fail
+            (ne, abs_diff / 2., 0),  # abs diff fail
+        ]
+
+        for op, _abs, _rel in tests:
+            assert op(np.array(actual), approx(expected, abs=_abs, rel=_rel))  # a, b
+            assert op(approx(expected, abs=_abs, rel=_rel), np.array(actual))  # b, a
+
+            assert op(actual, approx(np.array(expected), abs=_abs, rel=_rel))  # a, b
+            assert op(approx(np.array(expected), abs=_abs, rel=_rel), actual)  # b, a
+
+            assert op(np.array(actual), approx(np.array(expected), abs=_abs, rel=_rel))
+            assert op(approx(np.array(expected), abs=_abs, rel=_rel), np.array(actual))
+
+    def test_numpy_expecting_nan(self):
+        np = pytest.importorskip("numpy")
+        examples = [
+            (eq, nan, nan),
+            (eq, -nan, -nan),
+            (eq, nan, -nan),
+            (ne, 0.0, nan),
+            (ne, inf, nan),
+        ]
+        for op, a, x in examples:
+            # Nothing is equal to NaN by default.
+            assert np.array(a) != approx(x)
+            assert a != approx(np.array(x))
+
+            # If ``nan_ok=True``, then NaN is equal to NaN.
+            assert op(np.array(a), approx(x, nan_ok=True))
+            assert op(a, approx(np.array(x), nan_ok=True))
+
+    def test_numpy_expecting_inf(self):
+        np = pytest.importorskip("numpy")
+        examples = [
+            (eq, inf, inf),
+            (eq, -inf, -inf),
+            (ne, inf, -inf),
+            (ne, 0.0, inf),
+            (ne, nan, inf),
+        ]
+        for op, a, x in examples:
+            assert op(np.array(a), approx(x))
+            assert op(a, approx(np.array(x)))
+            assert op(np.array(a), approx(np.array(x)))
+
     def test_numpy_array_wrong_shape(self):
         np = pytest.importorskip("numpy")