diff --git a/news/6606.bugfix b/news/6606.bugfix
new file mode 100644
index 00000000000..3fbf7262f14
--- /dev/null
+++ b/news/6606.bugfix
@@ -0,0 +1 @@
+Fix bug that prevented installation of PEP 517 packages without ``setup.py``.
diff --git a/src/pip/_internal/commands/install.py b/src/pip/_internal/commands/install.py
index 66071f6e819..5842d18da1b 100644
--- a/src/pip/_internal/commands/install.py
+++ b/src/pip/_internal/commands/install.py
@@ -1,4 +1,3 @@
-
 # The following comment should be removed at some point in the future.
 # It's included for now because without it InstallCommand.run() has a
 # couple errors where we have to know req.name is str rather than
@@ -102,6 +101,8 @@ def get_check_binary_allowed(format_control):
     # type: (FormatControl) -> BinaryAllowedPredicate
     def check_binary_allowed(req):
         # type: (InstallRequirement) -> bool
+        if req.use_pep517:
+            return True
         canonical_name = canonicalize_name(req.name)
         allowed_formats = format_control.get_allowed_formats(canonical_name)
         return "binary" in allowed_formats
diff --git a/tests/data/packages/pep517_setup_and_pyproject/pyproject.toml b/tests/data/packages/pep517_setup_and_pyproject/pyproject.toml
new file mode 100644
index 00000000000..5a561e83317
--- /dev/null
+++ b/tests/data/packages/pep517_setup_and_pyproject/pyproject.toml
@@ -0,0 +1,3 @@
+[build-system]
+requires = [ "setuptools" ]
+build-backend = "setuptools.build_meta"
diff --git a/tests/data/packages/pep517_setup_and_pyproject/setup.cfg b/tests/data/packages/pep517_setup_and_pyproject/setup.cfg
new file mode 100644
index 00000000000..7eae9c0111e
--- /dev/null
+++ b/tests/data/packages/pep517_setup_and_pyproject/setup.cfg
@@ -0,0 +1,3 @@
+[metadata]
+name = pep517-setup-and-pyproject
+version = 1.0
diff --git a/tests/data/packages/pep517_setup_and_pyproject/setup.py b/tests/data/packages/pep517_setup_and_pyproject/setup.py
new file mode 100644
index 00000000000..606849326a4
--- /dev/null
+++ b/tests/data/packages/pep517_setup_and_pyproject/setup.py
@@ -0,0 +1,3 @@
+from setuptools import setup
+
+setup()
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index f07dcd4eff0..0bea0543f8b 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -1274,6 +1274,19 @@ def test_install_no_binary_disables_building_wheels(script, data, with_wheel):
     assert "Running setup.py install for upper" in str(res), str(res)
 
 
+def test_install_no_binary_builds_pep_517_wheel(script, data, with_wheel):
+    to_install = data.packages.joinpath('pep517_setup_and_pyproject')
+    res = script.pip(
+        'install', '--no-binary=:all:', '-f', data.find_links, to_install
+    )
+    expected = ("Successfully installed pep517-setup-and-pyproject")
+    # Must have installed the package
+    assert expected in str(res), str(res)
+
+    assert "Building wheel for pep517-setup" in str(res), str(res)
+    assert "Running setup.py install for pep517-set" not in str(res), str(res)
+
+
 def test_install_no_binary_disables_cached_wheels(script, data, with_wheel):
     # Seed the cache
     script.pip(