diff --git a/src/pip/_internal/index.py b/src/pip/_internal/index.py
index 43510fa9c..98b2b4c40 100644
--- a/src/pip/_internal/index.py
+++ b/src/pip/_internal/index.py
@@ -266,10 +266,24 @@ class CandidateEvaluator(object):
     def __init__(
         self,
         valid_tags,          # type: List[Pep425Tag]
-        prefer_binary=False  # type: bool
+        prefer_binary=False,   # type: bool
+        py_version_info=None,  # type: Optional[Tuple[int, ...]]
     ):
         # type: (...) -> None
+        """
+        :param py_version_info: The Python version, as a 3-tuple of ints
+            representing a major-minor-micro version, to use to check both
+            the Python version embedded in the filename and the package's
+            "Requires-Python" metadata. Defaults to `sys.version_info[:3]`.
+        """
+        if py_version_info is None:
+            py_version_info = sys.version_info[:3]
+
+        py_version = '.'.join(map(str, py_version_info[:2]))
+
         self._prefer_binary = prefer_binary
+        self._py_version = py_version
+        self._py_version_info = py_version_info
         self._valid_tags = valid_tags
 
         # We compile the regex here instead of as a class attribute so as
@@ -342,11 +356,11 @@ class CandidateEvaluator(object):
         if match:
             version = version[:match.start()]
             py_version = match.group(1)
-            if py_version != sys.version[:3]:
+            if py_version != self._py_version:
                 return (False, 'Python version is incorrect')
         try:
             support_this_python = check_requires_python(
-                link.requires_python, version_info=sys.version_info[:3],
+                link.requires_python, version_info=self._py_version_info,
             )
         except specifiers.InvalidSpecifier:
             logger.debug("Package %s has an invalid Requires-Python entry: %s",
diff --git a/tests/unit/test_index.py b/tests/unit/test_index.py
index 3bdd5695d..72c76b08a 100644
--- a/tests/unit/test_index.py
+++ b/tests/unit/test_index.py
@@ -1,5 +1,6 @@
 import logging
 import os.path
+import sys
 
 import pytest
 from mock import Mock
@@ -7,11 +8,36 @@ from pip._vendor import html5lib, requests
 
 from pip._internal.download import PipSession
 from pip._internal.index import (
-    Link, PackageFinder, _clean_link, _determine_base_url, _egg_info_matches,
-    _find_name_version_sep, _get_html_page,
+    CandidateEvaluator, Link, PackageFinder, _clean_link, _determine_base_url,
+    _egg_info_matches, _find_name_version_sep, _get_html_page,
 )
 
 
+class TestCandidateEvaluator:
+
+    @pytest.mark.parametrize("version_info, expected", [
+        ((2, 7, 14), '2.7'),
+        ((3, 6, 5), '3.6'),
+        # Check a minor version with two digits.
+        ((3, 10, 1), '3.10'),
+    ])
+    def test_init__py_version(self, version_info, expected):
+        """
+        Test the _py_version attribute.
+        """
+        evaluator = CandidateEvaluator([], py_version_info=version_info)
+        assert evaluator._py_version == expected
+
+    def test_init__py_version_default(self):
+        """
+        Test the _py_version attribute's default value.
+        """
+        evaluator = CandidateEvaluator([])
+        # Get the index of the second dot.
+        index = sys.version.find('.', 2)
+        assert evaluator._py_version == sys.version[:index]
+
+
 def test_sort_locations_file_expand_dir(data):
     """
     Test that a file:// dir gets listdir run with expand_dir