diff --git a/sphinx/builders/html/__init__.py b/sphinx/builders/html/__init__.py
index ad8436c932..7265370bb4 100644
--- a/sphinx/builders/html/__init__.py
+++ b/sphinx/builders/html/__init__.py
@@ -468,6 +468,16 @@ def prepare_writing(self, docnames: Set[str]) -> None:
         else:
             self.last_updated = None
 
+        # If the logo or favicon are urls, keep them as-is, otherwise
+        # strip the relative path as the files will be copied into _static.
+        logo = self.config.html_logo or ''
+        favicon = self.config.html_favicon or ''
+
+        if not isurl(logo):
+            logo = path.basename(logo)
+        if not isurl(favicon):
+            favicon = path.basename(favicon)
+
         self.relations = self.env.collect_relations()
 
         rellinks: List[Tuple[str, str, str, str]] = []
@@ -510,8 +520,8 @@ def prepare_writing(self, docnames: Set[str]) -> None:
             'rellinks': rellinks,
             'builder': self.name,
             'parents': [],
-            'logo': self.config.html_logo or '',
-            'favicon': self.config.html_favicon or '',
+            'logo': logo,
+            'favicon': favicon,
             'html5_doctype': html5_ready and not self.config.html4_writer,
         }
         if self.theme:
diff --git a/tests/roots/test-local-logo/conf.py b/tests/roots/test-local-logo/conf.py
new file mode 100644
index 0000000000..1a166c1305
--- /dev/null
+++ b/tests/roots/test-local-logo/conf.py
@@ -0,0 +1,4 @@
+latex_documents = [
+    ('index', 'test.tex', 'The basic Sphinx documentation for testing', 'Sphinx', 'report')
+]
+html_logo = "images/img.png"
diff --git a/tests/roots/test-local-logo/images/img.png b/tests/roots/test-local-logo/images/img.png
new file mode 100644
index 0000000000..a97e86d66a
Binary files /dev/null and b/tests/roots/test-local-logo/images/img.png differ
diff --git a/tests/roots/test-local-logo/index.rst b/tests/roots/test-local-logo/index.rst
new file mode 100644
index 0000000000..48407e643c
--- /dev/null
+++ b/tests/roots/test-local-logo/index.rst
@@ -0,0 +1,32 @@
+The basic Sphinx documentation for testing
+==========================================
+
+Sphinx is a tool that makes it easy to create intelligent and beautiful
+documentation for Python projects (or other documents consisting of multiple
+reStructuredText sources), written by Georg Brandl.  It was originally created
+for the new Python documentation, and has excellent facilities for Python
+project documentation, but C/C++ is supported as well, and more languages are
+planned.
+
+Sphinx uses reStructuredText as its markup language, and many of its strengths
+come from the power and straightforwardness of reStructuredText and its parsing
+and translating suite, the Docutils.
+
+features
+--------
+
+Among its features are the following:
+
+* Output formats: HTML (including derivative formats such as HTML Help, Epub
+  and Qt Help), plain text, manual pages and LaTeX or direct PDF output
+  using rst2pdf
+* Extensive cross-references: semantic markup and automatic links
+  for functions, classes, glossary terms and similar pieces of information
+* Hierarchical structure: easy definition of a document tree, with automatic
+  links to siblings, parents and children
+* Automatic indices: general index as well as a module index
+* Code handling: automatic highlighting using the Pygments highlighter
+* Flexible HTML output using the Jinja 2 templating engine
+* Various extensions are available, e.g. for automatic testing of snippets
+  and inclusion of appropriately formatted docstrings
+* Setuptools integration
diff --git a/tests/test_build_html.py b/tests/test_build_html.py
index e74319f198..d295cf982c 100644
--- a/tests/test_build_html.py
+++ b/tests/test_build_html.py
@@ -1340,6 +1340,15 @@ def test_html_remote_logo(app, status, warning):
     assert not (app.outdir / 'python-logo.png').exists()
 
 
+@pytest.mark.sphinx('html', testroot='local-logo')
+def test_html_local_logo(app, status, warning):
+    app.builder.build_all()
+
+    result = (app.outdir / 'index.html').read_text()
+    assert ('<img class="logo" src="_static/img.png" alt="Logo"/>' in result)
+    assert (app.outdir / '_static/img.png').exists()
+
+
 @pytest.mark.sphinx('html', testroot='basic')
 def test_html_sidebar(app, status, warning):
     ctx = {}