diff --git a/babel/messages/catalog.py b/babel/messages/catalog.py
index 9f215cf18..ecf6f91d4 100644
--- a/babel/messages/catalog.py
+++ b/babel/messages/catalog.py
@@ -479,7 +479,11 @@ def _set_mime_headers(self, headers: Iterable[tuple[str, str]]) -> None:
                 self.last_translator = value
             elif name == 'language':
                 value = value.replace('-', '_')
-                self._set_locale(value)
+                # The `or None` makes sure that the locale is set to None
+                # if the header's value is an empty string, which is what
+                # some tools generate (instead of eliding the empty Language
+                # header altogether).
+                self._set_locale(value or None)
             elif name == 'language-team':
                 self.language_team = value
             elif name == 'content-type':
diff --git a/tests/messages/test_pofile.py b/tests/messages/test_pofile.py
index 99958b7b7..d1a3e2d11 100644
--- a/tests/messages/test_pofile.py
+++ b/tests/messages/test_pofile.py
@@ -893,3 +893,12 @@ def test_iterable_of_strings():
     catalog = pofile.read_po(['msgid "foo"', b'msgstr "Voh"'], locale="en_US")
     assert catalog.locale == Locale("en", "US")
     assert catalog.get("foo").string == "Voh"
+
+
+def test_issue_1087():
+    buf = StringIO(r'''
+msgid ""
+msgstr ""
+"Language: \n"
+''')
+    assert pofile.read_po(buf).locale is None