diff --git a/AUTHORS b/AUTHORS
index 25b55e5ae..283813f15 100644
--- a/AUTHORS
+++ b/AUTHORS
@@ -321,6 +321,7 @@ Thomas Grainger
 Thomas Hisch
 Tim Hoffmann
 Tim Strazny
+Tobias Deiminger
 Tom Dalton
 Tom Viner
 Tomáš Gavenčiak
diff --git a/changelog/8914.bugfix.rst b/changelog/8914.bugfix.rst
new file mode 100644
index 000000000..2302ad0c8
--- /dev/null
+++ b/changelog/8914.bugfix.rst
@@ -0,0 +1,3 @@
+If fixtures had been indirectly parameterized via test function, e.g. using a
+``@pytest.mark.parametrize(indirect=True)`` marker, reordering of tests for the least possible fixture setup/teardown cycles
+did not work. Optimized test groups can now be determined given the user provided parameter type is hashable.
diff --git a/src/_pytest/fixtures.py b/src/_pytest/fixtures.py
index e0409fcf2..80758205b 100644
--- a/src/_pytest/fixtures.py
+++ b/src/_pytest/fixtures.py
@@ -5,6 +5,7 @@ import sys
 import warnings
 from collections import defaultdict
 from collections import deque
+from collections.abc import Hashable
 from contextlib import suppress
 from pathlib import Path
 from types import TracebackType
@@ -238,6 +239,23 @@ def getfixturemarker(obj: object) -> Optional["FixtureFunctionMarker"]:
 _Key = Tuple[object, ...]
 
 
+@attr.s(auto_attribs=True, eq=False, slots=True)
+class SafeHashWrapper:
+    obj: Any
+
+    def __eq__(self, other: object) -> bool:
+        try:
+            res = self.obj == other
+            return bool(res)
+        except Exception:
+            return id(self.obj) == id(other)
+
+    def __hash__(self) -> int:
+        if isinstance(self.obj, Hashable):
+            return hash(self.obj)
+        return hash(id(self.obj))
+
+
 def get_parametrized_fixture_keys(item: nodes.Item, scope: Scope) -> Iterator[_Key]:
     """Return list of keys for all parametrized arguments which match
     the specified scope."""
@@ -254,15 +272,19 @@ def get_parametrized_fixture_keys(item: nodes.Item, scope: Scope) -> Iterator[_K
         for argname, param_index in sorted(cs.indices.items()):
             if cs._arg2scope[argname] != scope:
                 continue
+            # param ends up inside a dict key, and therefore must be hashable.
+            # Parameter values are possibly unhashable (dicts, numpy arrays, ...).
+            # SafeHashWrapper makes them hashable by a fallback to their identity.
+            param = SafeHashWrapper(cs.params[argname])
             if scope is Scope.Session:
-                key: _Key = (argname, param_index)
+                key: _Key = (argname, param)
             elif scope is Scope.Package:
-                key = (argname, param_index, item.path.parent)
+                key = (argname, param, item.path.parent)
             elif scope is Scope.Module:
-                key = (argname, param_index, item.path)
+                key = (argname, param, item.path)
             elif scope is Scope.Class:
                 item_cls = item.cls  # type: ignore[attr-defined]
-                key = (argname, param_index, item.path, item_cls)
+                key = (argname, param, item.path, item_cls)
             else:
                 assert_never(scope)
             yield key
diff --git a/testing/example_scripts/issue_519.py b/testing/example_scripts/issue_519.py
index e44367fca..73437ef7b 100644
--- a/testing/example_scripts/issue_519.py
+++ b/testing/example_scripts/issue_519.py
@@ -22,13 +22,13 @@ def checked_order():
     assert order == [
         ("issue_519.py", "fix1", "arg1v1"),
         ("test_one[arg1v1-arg2v1]", "fix2", "arg2v1"),
-        ("test_two[arg1v1-arg2v1]", "fix2", "arg2v1"),
         ("test_one[arg1v1-arg2v2]", "fix2", "arg2v2"),
+        ("test_two[arg1v1-arg2v1]", "fix2", "arg2v1"),
         ("test_two[arg1v1-arg2v2]", "fix2", "arg2v2"),
         ("issue_519.py", "fix1", "arg1v2"),
         ("test_one[arg1v2-arg2v1]", "fix2", "arg2v1"),
-        ("test_two[arg1v2-arg2v1]", "fix2", "arg2v1"),
         ("test_one[arg1v2-arg2v2]", "fix2", "arg2v2"),
+        ("test_two[arg1v2-arg2v1]", "fix2", "arg2v1"),
         ("test_two[arg1v2-arg2v2]", "fix2", "arg2v2"),
     ]
 
diff --git a/testing/python/fixtures.py b/testing/python/fixtures.py
index 3ce5cb34d..f9e6635e2 100644
--- a/testing/python/fixtures.py
+++ b/testing/python/fixtures.py
@@ -1308,6 +1308,34 @@ class TestFixtureUsages:
         result = pytester.runpytest()
         result.stdout.fnmatch_lines(["*4 passed*"])
 
+    def test_optimize_by_reorder_indirect(self, pytester: Pytester) -> None:
+        """Test reordering for minimal setup/teardown with indirectly parametrized fixtures. See #8914, #9350."""
+        pytester.makepyfile(
+            """
+            import pytest
+
+            @pytest.fixture(scope="session")
+            def fix(request):
+                print(f'prepare foo-%s' % request.param)
+                yield request.param
+                print(f'teardown foo-%s' % request.param)
+
+            @pytest.mark.parametrize("fix", ["data1", "data2"], indirect=True)
+            def test1(fix):
+                pass
+
+            @pytest.mark.parametrize("fix", ["data2", "data1"], indirect=True)
+            def test2(fix):
+                pass
+        """
+        )
+        result = pytester.runpytest("-s")
+        output = result.stdout.str()
+        assert output.count("prepare foo-data1") == 1
+        assert output.count("prepare foo-data2") == 1
+        assert output.count("teardown foo-data1") == 1
+        assert output.count("teardown foo-data2") == 1
+
     def test_funcarg_parametrized_and_used_twice(self, pytester: Pytester) -> None:
         pytester.makepyfile(
             """