diff --git a/news/6642.bugfix b/news/6642.bugfix
new file mode 100644
index 000000000..470572ad6
--- /dev/null
+++ b/news/6642.bugfix
@@ -0,0 +1,2 @@
+Do not attempt to run ``setup.py clean`` after a ``pep517`` build error,
+since a ``setup.py`` may not exist in that case.
diff --git a/src/pip/_internal/wheel_builder.py b/src/pip/_internal/wheel_builder.py
index b992bd676..35e4f9eff 100644
--- a/src/pip/_internal/wheel_builder.py
+++ b/src/pip/_internal/wheel_builder.py
@@ -231,11 +231,12 @@ def _build_one_inside_env(
                     req.name, e,
                 )
         # Ignore return, we can't do anything else useful.
-        _clean_one(req, global_options)
+        if not req.use_pep517:
+            _clean_one_legacy(req, global_options)
         return None
 
 
-def _clean_one(req, global_options):
+def _clean_one_legacy(req, global_options):
     # type: (InstallRequirement, List[str]) -> bool
     clean_args = make_setuptools_clean_args(
         req.setup_py_path,
diff --git a/tests/data/packages/pep517_wrapper_buildsys/mybuildsys.py b/tests/data/packages/pep517_wrapper_buildsys/mybuildsys.py
index df391e96a..e2f920ba3 100644
--- a/tests/data/packages/pep517_wrapper_buildsys/mybuildsys.py
+++ b/tests/data/packages/pep517_wrapper_buildsys/mybuildsys.py
@@ -8,6 +8,9 @@ from setuptools.build_meta import (get_requires_for_build_sdist,
 
 
 def build_wheel(*a, **kw):
+    if os.environ.get("PIP_TEST_FAIL_BUILD_WHEEL"):
+        raise RuntimeError("Failing build_wheel, as requested.")
+
     # Create the marker file to record that the hook was called
     with open(os.environ['PIP_TEST_MARKER_FILE'], 'wb'):
         pass
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index 8ae64319d..5548d792c 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1256,6 +1256,7 @@ def test_cleanup_after_failed_wheel(script, with_wheel):
     shebang = open(script_py, 'r').readline().strip()
     assert shebang != '#!python', shebang
     # OK, assert that we *said* we were cleaning up:
+    # /!\ if in need to change this, also change test_pep517_no_legacy_cleanup
     assert "Running setup.py clean for wheelbrokenafter" in str(res), str(res)
 
 
diff --git a/tests/functional/test_install_cleanup.py b/tests/functional/test_install_cleanup.py
index dc87bc3f7..c6464e3ee 100644
--- a/tests/functional/test_install_cleanup.py
+++ b/tests/functional/test_install_cleanup.py
@@ -136,3 +136,19 @@ def test_cleanup_prevented_upon_build_dir_exception(script, data):
     assert result.returncode == PREVIOUS_BUILD_DIR_ERROR, str(result)
     assert "pip can't proceed" in result.stderr, str(result)
     assert exists(build_simple), str(result)
+
+
+@pytest.mark.network
+def test_pep517_no_legacy_cleanup(script, data, with_wheel):
+    """Test a PEP 517 failed build does not attempt a legacy cleanup"""
+    to_install = data.packages.joinpath('pep517_wrapper_buildsys')
+    script.environ["PIP_TEST_FAIL_BUILD_WHEEL"] = "1"
+    res = script.pip(
+        'install', '-f', data.find_links, to_install,
+        expect_error=True
+    )
+    # Must not have built the package
+    expected = "Failed building wheel for pep517-wrapper-buildsys"
+    assert expected in str(res)
+    # Must not have attempted legacy cleanup
+    assert "setup.py clean" not in str(res)