diff --git a/news/5716.bugfix b/news/5716.bugfix
new file mode 100644
index 00000000000..1b705df6f92
--- /dev/null
+++ b/news/5716.bugfix
@@ -0,0 +1 @@
+Fix case sensitive comparison of pip freeze when used with -r option.
\ No newline at end of file
diff --git a/src/pip/_internal/operations/freeze.py b/src/pip/_internal/operations/freeze.py
index 6eaa85b19ec..441c66b8a72 100644
--- a/src/pip/_internal/operations/freeze.py
+++ b/src/pip/_internal/operations/freeze.py
@@ -79,7 +79,7 @@ def freeze(
             continue
         if exclude_editable and req.editable:
             continue
-        installations[req.name] = req
+        installations[req.canonical_name] = req
 
     if requirement:
         # the options that don't get turned into an InstallRequirement
@@ -138,22 +138,24 @@ def freeze(
                             "  (add #egg=PackageName to the URL to avoid"
                             " this warning)"
                         )
-                    elif line_req.name not in installations:
-                        # either it's not installed, or it is installed
-                        # but has been processed already
-                        if not req_files[line_req.name]:
-                            logger.warning(
-                                "Requirement file [%s] contains %s, but "
-                                "package %r is not installed",
-                                req_file_path,
-                                COMMENT_RE.sub('', line).strip(), line_req.name
-                            )
+                    else:
+                        line_req_canonical_name = canonicalize_name(line_req.name)
+                        if line_req_canonical_name not in installations:
+                            # either it's not installed, or it is installed
+                            # but has been processed already
+                            if not req_files[line_req.name]:
+                                logger.warning(
+                                    "Requirement file [%s] contains %s, but "
+                                    "package %r is not installed",
+                                    req_file_path,
+                                    COMMENT_RE.sub('', line).strip(), line_req.name
+                                )
+                            else:
+                                req_files[line_req.name].append(req_file_path)
                         else:
+                            yield str(installations[line_req_canonical_name]).rstrip()
+                            del installations[line_req_canonical_name]
                             req_files[line_req.name].append(req_file_path)
-                    else:
-                        yield str(installations[line_req.name]).rstrip()
-                        del installations[line_req.name]
-                        req_files[line_req.name].append(req_file_path)
 
         # Warn about requirements that were included multiple times (in a
         # single requirements file or in different requirements files).
@@ -168,7 +170,7 @@ def freeze(
         )
     for installation in sorted(
             installations.values(), key=lambda x: x.name.lower()):
-        if canonicalize_name(installation.name) not in skip:
+        if installation.canonical_name not in skip:
             yield str(installation).rstrip()
 
 
@@ -238,6 +240,7 @@ class FrozenRequirement(object):
     def __init__(self, name, req, editable, comments=()):
         # type: (str, Union[str, Requirement], bool, Iterable[str]) -> None
         self.name = name
+        self.canonical_name = canonicalize_name(name)
         self.req = req
         self.editable = editable
         self.comments = comments
diff --git a/tests/functional/test_freeze.py b/tests/functional/test_freeze.py
index 77f83796abc..98d04f2802b 100644
--- a/tests/functional/test_freeze.py
+++ b/tests/functional/test_freeze.py
@@ -502,15 +502,20 @@ def test_freeze_with_requirement_option(script):
 
     """
 
-    script.scratch_path.joinpath("hint.txt").write_text(textwrap.dedent("""\
+    script.scratch_path.joinpath("hint1.txt").write_text(textwrap.dedent("""\
         INITools==0.1
         NoExist==4.2  # A comment that ensures end of line comments work.
         simple==3.0; python_version > '1.0'
         """) + _freeze_req_opts)
+    script.scratch_path.joinpath("hint2.txt").write_text(textwrap.dedent("""\
+        iniTools==0.1
+        Noexist==4.2  # A comment that ensures end of line comments work.
+        Simple==3.0; python_version > '1.0'
+        """) + _freeze_req_opts)
     result = script.pip_install_local('initools==0.2')
     result = script.pip_install_local('simple')
     result = script.pip(
-        'freeze', '--requirement', 'hint.txt',
+        'freeze', '--requirement', 'hint1.txt',
         expect_stderr=True,
     )
     expected = textwrap.dedent("""\
@@ -524,6 +529,15 @@ def test_freeze_with_requirement_option(script):
         "Requirement file [hint.txt] contains NoExist==4.2, but package "
         "'NoExist' is not installed"
     ) in result.stderr
+    result = script.pip(
+        'freeze', '--requirement', 'hint2.txt',
+        expect_stderr=True,
+    )
+    _check_output(result.stdout, expected)
+    assert (
+        "Requirement file [hint.txt] contains NoExist==4.2, but package "
+        "'NoExist' is not installed"
+    ) in result.stderr
 
 
 def test_freeze_with_requirement_option_multiple(script):