diff --git a/CHANGES b/CHANGES
index 65d237fc6..e8ee9e4d0 100644
--- a/CHANGES
+++ b/CHANGES
@@ -34,6 +34,7 @@ Bugs fixed
   :file:`parskip.sty`
 * #5958: versionadded directive causes crash with Python 3.5.0
 * #5995: autodoc: autodoc_mock_imports conflict with metaclass on Python 3.7
+* #5871: texinfo: a section title ``.`` is not allowed
 
 Testing
 --------
diff --git a/sphinx/writers/texinfo.py b/sphinx/writers/texinfo.py
index d7490a652..63c7d2af8 100644
--- a/sphinx/writers/texinfo.py
+++ b/sphinx/writers/texinfo.py
@@ -384,9 +384,12 @@ class TexinfoTranslator(nodes.NodeVisitor):
     def escape_id(self, s):
         # type: (unicode) -> unicode
         """Return an escaped string suitable for node names and anchors."""
-        bad_chars = ',:.()'
+        bad_chars = ',:()'
         for bc in bad_chars:
             s = s.replace(bc, ' ')
+        if re.search('[^ .]', s):
+            # remove DOTs if name contains other characters
+            s = s.replace('.', ' ')
         s = ' '.join(s.split()).strip()
         return self.escape(s)
 
diff --git a/tests/test_build_texinfo.py b/tests/test_build_texinfo.py
index d7b7e520a..93e10d758 100644
--- a/tests/test_build_texinfo.py
+++ b/tests/test_build_texinfo.py
@@ -15,10 +15,12 @@ import re
 from subprocess import Popen, PIPE
 
 import pytest
+from mock import Mock
 from six import PY3
 from test_build_html import ENV_WARNINGS
 
 from sphinx.testing.util import remove_unicode_literals, strip_escseq
+from sphinx.util.docutils import new_document
 from sphinx.writers.texinfo import TexinfoTranslator
 
 
@@ -93,3 +95,20 @@ def test_texinfo_citation(app, status, warning):
             'This is a citation\n') in output
     assert ('@anchor{index cite2}@anchor{2}@w{(CITE2)} \n'
             'This is a multiline citation\n') in output
+
+
+@pytest.mark.sphinx('texinfo')
+def test_texinfo_escape_id(app, status, warning):
+    settings = Mock(title='',
+                    texinfo_dir_entry='',
+                    texinfo_elements={})
+    document = new_document('', settings)
+    translator = app.builder.create_translator(document, app.builder)
+
+    assert translator.escape_id('Hello world') == 'Hello world'
+    assert translator.escape_id('Hello    world') == 'Hello world'
+    assert translator.escape_id('Hello   Sphinx   world') == 'Hello Sphinx world'
+    assert translator.escape_id('Hello:world') == 'Hello world'
+    assert translator.escape_id('Hello(world)') == 'Hello world'
+    assert translator.escape_id('Hello world.') == 'Hello world'
+    assert translator.escape_id('.') == '.'