diff --git a/news/8724.bugfix b/news/8724.bugfix
new file mode 100644
index 00000000000..8641098dde6
--- /dev/null
+++ b/news/8724.bugfix
@@ -0,0 +1,2 @@
+2020 Resolver: Correctly handle marker evaluation in constraints and exclude
+them if their markers do not match the current environment.
diff --git a/src/pip/_internal/resolution/resolvelib/resolver.py b/src/pip/_internal/resolution/resolvelib/resolver.py
index 43ea248632d..aecddb1138c 100644
--- a/src/pip/_internal/resolution/resolvelib/resolver.py
+++ b/src/pip/_internal/resolution/resolvelib/resolver.py
@@ -90,7 +90,8 @@ def resolve(self, root_reqs, check_supported_wheels):
                 problem = check_invalid_constraint_type(req)
                 if problem:
                     raise InstallationError(problem)
-
+                if not req.match_markers():
+                    continue
                 name = canonicalize_name(req.name)
                 if name in constraints:
                     constraints[name] = constraints[name] & req.specifier
diff --git a/tests/functional/test_new_resolver.py b/tests/functional/test_new_resolver.py
index 9329180334c..46e32ddd3d7 100644
--- a/tests/functional/test_new_resolver.py
+++ b/tests/functional/test_new_resolver.py
@@ -1,6 +1,7 @@
 import json
 import os
 import sys
+import textwrap
 
 import pytest
 from pip._vendor.packaging.utils import canonicalize_name
@@ -729,6 +730,30 @@ def test_new_resolver_constraint_on_path(script):
     assert msg in result.stderr, str(result)
 
 
+def test_new_resolver_constraint_only_marker_match(script):
+    create_basic_wheel_for_package(script, "pkg", "1.0")
+    create_basic_wheel_for_package(script, "pkg", "2.0")
+    create_basic_wheel_for_package(script, "pkg", "3.0")
+
+    constrants_content = textwrap.dedent(
+        """
+        pkg==1.0; python_version == "{ver[0]}.{ver[1]}"  # Always satisfies.
+        pkg==2.0; python_version < "0"  # Never satisfies.
+        """
+    ).format(ver=sys.version_info)
+    constraints_txt = script.scratch_path / "constraints.txt"
+    constraints_txt.write_text(constrants_content)
+
+    script.pip(
+        "install", "--use-feature=2020-resolver",
+        "--no-cache-dir", "--no-index",
+        "-c", constraints_txt,
+        "--find-links", script.scratch_path,
+        "pkg",
+    )
+    assert_installed(script, pkg="1.0")
+
+
 def test_new_resolver_upgrade_needs_option(script):
     # Install pkg 1.0.0
     create_basic_wheel_for_package(script, "pkg", "1.0.0")