diff --git a/src/pip/_internal/req/constructors.py b/src/pip/_internal/req/constructors.py
index bc10760077f..052ac2cabba 100644
--- a/src/pip/_internal/req/constructors.py
+++ b/src/pip/_internal/req/constructors.py
@@ -435,21 +435,20 @@ def install_req_from_req_string(
         )
 
     if req.url:
-        # Create an InstallRequirement for a PEP 508 URL with the same behavior
-        # as 'pip install req.url'
-        parts = parse_req_from_line(req.url, None)
-        constraint = False
-
-        return InstallRequirement(
-            parts.requirement,
-            comes_from,
-            link=parts.link,
-            markers=parts.markers,
-            use_pep517=use_pep517,
-            isolated=isolated,
-            constraint=constraint,
-            extras=req.extras,
-        )
+        # Create an InstallRequirement for a wheel-like PEP 508 URL with the
+        # same behavior as 'pip install req.url'
+        parts = parse_req_from_line(req.url, comes_from)
+        link = Link(req.url)
+        if link.is_wheel:
+            return InstallRequirement(
+                parts.requirement,
+                comes_from=comes_from,
+                link=parts.link,
+                markers=parts.markers,
+                use_pep517=use_pep517,
+                isolated=isolated,
+                extras=req.extras,
+            )
     return InstallRequirement(
         req, comes_from, isolated=isolated, use_pep517=use_pep517
     )
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index b74a9abf709..4d03ced5be2 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1623,44 +1623,6 @@ def test_install_pep508_with_url_in_install_requires_url_change_wheel(script):
     assert "Requirement already satisfied: dep==2.0" in str(res), str(res)
 
 
-def test_install_pep508_with_url_in_install_requires_url_change_directory(
-        script):
-    dep_v1_path = create_test_package_with_setup(
-        script, name='dep', version='1.0',
-    )
-
-    # Rename the package directory so it doesn't get overwritten when
-    # creating the package for dep_v2
-    dep_v1_path.rename(dep_v1_path.parent / 'dep_v1')
-    dep_v1_path = dep_v1_path.parent / 'dep_v1'
-
-    dep_v2_path = create_test_package_with_setup(
-        script, name='dep', version='2.0',
-    )
-
-    pkga_path = create_basic_wheel_for_package(
-        script, name='pkga', version='1.0',
-        depends=['dep@' + path_to_url(dep_v1_path)],
-    )
-    res = script.pip('install', pkga_path)
-    assert "Successfully installed dep-1.0" in str(res), str(res)
-
-    pkga_path.unlink()
-
-    # Updating the URL to the dependency installs the updated dependency
-    pkga_path = create_basic_wheel_for_package(
-        script, name='pkga', version='2.0',
-        depends=['dep@' + path_to_url(dep_v2_path)],
-    )
-    res = script.pip('install', pkga_path)
-    assert "Successfully installed dep-2.0" in str(res), str(res)
-
-    res = script.pip('install', pkga_path)
-    # pip can't determine versions from a directory name, so it will always
-    # reinstall the dependency
-    assert "Successfully installed dep-2.0" in str(res), str(res)
-
-
 @pytest.mark.network
 @pytest.mark.parametrize('index', (PyPI.simple_url, TestPyPI.simple_url))
 def test_install_from_test_pypi_with_ext_url_dep_is_blocked(script, index):
diff --git a/tests/unit/test_req_install.py b/tests/unit/test_req_install.py
index 309370326b2..ef0ab68858a 100644
--- a/tests/unit/test_req_install.py
+++ b/tests/unit/test_req_install.py
@@ -8,7 +8,6 @@
 from pip._internal.req.constructors import (
     install_req_from_line,
     install_req_from_req_string,
-    path_to_url,
 )
 from pip._internal.req.req_install import InstallRequirement
 
@@ -151,22 +150,3 @@ def test_install_req_from_string_pep508_url_wheel_extras(self, use_pep517):
         assert install_req.is_wheel
         assert install_req.use_pep517 == use_pep517
         assert install_req.extras == {"security"}
-
-    @pytest.mark.parametrize("use_pep517", [None, True, False])
-    def test_install_req_from_string_pep508_url_not_a_wheel(
-            self, use_pep517, tmpdir):
-        """
-        install_req_from_string returns an InstallRequirement() with
-        ``.req = None`` so that the package is always reinstalled.
-        """
-        file_url = path_to_url(tmpdir / "fake_torch_package")
-        install_str = "torch@ " + file_url
-        install_req = install_req_from_req_string(
-            install_str, use_pep517=use_pep517
-        )
-
-        assert isinstance(install_req, InstallRequirement)
-        assert install_req.req is None
-        assert install_req.link.url == file_url
-        assert not install_req.is_wheel
-        assert install_req.use_pep517 == use_pep517