diff --git a/changelog/5036.bugfix.rst b/changelog/5036.bugfix.rst
new file mode 100644
index 000000000..a9c266538
--- /dev/null
+++ b/changelog/5036.bugfix.rst
@@ -0,0 +1 @@
+Fix issue where fixtures dependent on other parametrized fixtures would be erroneously parametrized.
diff --git a/src/_pytest/fixtures.py b/src/_pytest/fixtures.py
index 7761c4af8..fa2974f1b 100644
--- a/src/_pytest/fixtures.py
+++ b/src/_pytest/fixtures.py
@@ -1129,18 +1129,40 @@ class FixtureManager(object):
         self._nodeid_and_autousenames = [("", self.config.getini("usefixtures"))]
         session.config.pluginmanager.register(self, "funcmanage")
 
+    def _get_direct_parametrize_args(self, node):
+        """This function returns all the direct parametrization
+        arguments of a node, so we don't mistake them for fixtures
+
+        Check https://github.com/pytest-dev/pytest/issues/5036
+
+        This things are done later as well when dealing with parametrization
+        so this could be improved
+        """
+        from _pytest.mark import ParameterSet
+
+        parametrize_argnames = []
+        for marker in node.iter_markers(name="parametrize"):
+            if not marker.kwargs.get("indirect", False):
+                p_argnames, _ = ParameterSet._parse_parametrize_args(
+                    *marker.args, **marker.kwargs
+                )
+                parametrize_argnames.extend(p_argnames)
+
+        return parametrize_argnames
+
     def getfixtureinfo(self, node, func, cls, funcargs=True):
         if funcargs and not getattr(node, "nofuncargs", False):
             argnames = getfuncargnames(func, cls=cls)
         else:
             argnames = ()
+
         usefixtures = itertools.chain.from_iterable(
             mark.args for mark in node.iter_markers(name="usefixtures")
         )
         initialnames = tuple(usefixtures) + argnames
         fm = node.session._fixturemanager
         initialnames, names_closure, arg2fixturedefs = fm.getfixtureclosure(
-            initialnames, node
+            initialnames, node, ignore_args=self._get_direct_parametrize_args(node)
         )
         return FuncFixtureInfo(argnames, initialnames, names_closure, arg2fixturedefs)
 
@@ -1174,7 +1196,7 @@ class FixtureManager(object):
                 autousenames.extend(basenames)
         return autousenames
 
-    def getfixtureclosure(self, fixturenames, parentnode):
+    def getfixtureclosure(self, fixturenames, parentnode, ignore_args=()):
         # collect the closure of all fixtures , starting with the given
         # fixturenames as the initial set.  As we have to visit all
         # factory definitions anyway, we also return an arg2fixturedefs
@@ -1202,6 +1224,8 @@ class FixtureManager(object):
         while lastlen != len(fixturenames_closure):
             lastlen = len(fixturenames_closure)
             for argname in fixturenames_closure:
+                if argname in ignore_args:
+                    continue
                 if argname in arg2fixturedefs:
                     continue
                 fixturedefs = self.getfixturedefs(argname, parentid)
diff --git a/src/_pytest/mark/structures.py b/src/_pytest/mark/structures.py
index b133a4e26..561ccc3f4 100644
--- a/src/_pytest/mark/structures.py
+++ b/src/_pytest/mark/structures.py
@@ -103,8 +103,11 @@ class ParameterSet(namedtuple("ParameterSet", "values, marks, id")):
         else:
             return cls(parameterset, marks=[], id=None)
 
-    @classmethod
-    def _for_parametrize(cls, argnames, argvalues, func, config, function_definition):
+    @staticmethod
+    def _parse_parametrize_args(argnames, argvalues, **_):
+        """It receives an ignored _ (kwargs) argument so this function can
+        take also calls from parametrize ignoring scope, indirect, and other
+        arguments..."""
         if not isinstance(argnames, (tuple, list)):
             argnames = [x.strip() for x in argnames.split(",") if x.strip()]
             force_tuple = len(argnames) == 1
@@ -113,6 +116,11 @@ class ParameterSet(namedtuple("ParameterSet", "values, marks, id")):
         parameters = [
             ParameterSet.extract_from(x, force_tuple=force_tuple) for x in argvalues
         ]
+        return argnames, parameters
+
+    @classmethod
+    def _for_parametrize(cls, argnames, argvalues, func, config, function_definition):
+        argnames, parameters = cls._parse_parametrize_args(argnames, argvalues)
         del argvalues
 
         if parameters:
diff --git a/testing/python/fixtures.py b/testing/python/fixtures.py
index 18ede4006..bd1b1d975 100644
--- a/testing/python/fixtures.py
+++ b/testing/python/fixtures.py
@@ -3950,3 +3950,46 @@ def test_call_fixture_function_error():
 
     with pytest.raises(pytest.fail.Exception):
         assert fix() == 1
+
+
+def test_fixture_param_shadowing(testdir):
+    """Parametrized arguments would be shadowed if a fixture with the same name also exists (#5036)"""
+    testdir.makepyfile(
+        """
+        import pytest
+
+        @pytest.fixture(params=['a', 'b'])
+        def argroot(request):
+            return request.param
+
+        @pytest.fixture
+        def arg(argroot):
+            return argroot
+
+        # This should only be parametrized directly
+        @pytest.mark.parametrize("arg", [1])
+        def test_direct(arg):
+            assert arg == 1
+
+        # This should be parametrized based on the fixtures
+        def test_normal_fixture(arg):
+            assert isinstance(arg, str)
+
+        # Indirect should still work:
+
+        @pytest.fixture
+        def arg2(request):
+            return 2*request.param
+
+        @pytest.mark.parametrize("arg2", [1], indirect=True)
+        def test_indirect(arg2):
+            assert arg2 == 2
+    """
+    )
+    # Only one test should have run
+    result = testdir.runpytest("-v")
+    result.assert_outcomes(passed=4)
+    result.stdout.fnmatch_lines(["*::test_direct[[]1[]]*"])
+    result.stdout.fnmatch_lines(["*::test_normal_fixture[[]a[]]*"])
+    result.stdout.fnmatch_lines(["*::test_normal_fixture[[]b[]]*"])
+    result.stdout.fnmatch_lines(["*::test_indirect[[]1[]]*"])