diff --git a/sphinx/testing/fixtures.py b/sphinx/testing/fixtures.py
index eaf76e284..a62f34694 100644
--- a/sphinx/testing/fixtures.py
+++ b/sphinx/testing/fixtures.py
@@ -7,15 +7,16 @@ import subprocess
 import sys
 from collections import namedtuple
 from io import StringIO
-from typing import TYPE_CHECKING, Any, Callable
+from typing import TYPE_CHECKING, Optional
 
 import pytest
 
 from sphinx.testing.util import SphinxTestApp, SphinxTestAppWrapperForSkipBuilding
 
 if TYPE_CHECKING:
-    from collections.abc import Generator
+    from collections.abc import Callable, Generator
     from pathlib import Path
+    from typing import Any
 
 DEFAULT_ENABLED_MARKERS = [
     (
@@ -60,8 +61,13 @@ class SharedResult:
 
 
 @pytest.fixture()
-def app_params(request: Any, test_params: dict, shared_result: SharedResult,
-               sphinx_test_tempdir: str, rootdir: str) -> _app_params:
+def app_params(
+    request: Any,
+    test_params: dict,
+    shared_result: SharedResult,
+    sphinx_test_tempdir: str,
+    rootdir: str,
+) -> _app_params:
     """
     Parameters that are specified by 'pytest.mark.sphinx' for
     sphinx.application.Sphinx initialization
@@ -128,8 +134,12 @@ def test_params(request: Any) -> dict:
 
 
 @pytest.fixture()
-def app(test_params: dict, app_params: tuple[dict, dict], make_app: Callable,
-        shared_result: SharedResult) -> Generator[SphinxTestApp, None, None]:
+def app(
+    test_params: dict,
+    app_params: tuple[dict, dict],
+    make_app: Callable,
+    shared_result: SharedResult,
+) -> Generator[SphinxTestApp, None, None]:
     """
     Provides the 'sphinx.application.Sphinx' object
     """
@@ -218,6 +228,52 @@ def if_graphviz_found(app: SphinxTestApp) -> None:  # NoQA: PT004
     pytest.skip('graphviz "dot" is not available')
 
 
+_HOST_ONLINE_ERROR = pytest.StashKey[Optional[str]]()
+
+
+def _query(address: tuple[str, int]) -> str | None:
+    import socket
+
+    with socket.socket(socket.AF_INET, socket.SOCK_STREAM) as sock:
+        try:
+            sock.settimeout(5)
+            sock.connect(address)
+        except OSError as exc:
+            # other type of errors are propagated
+            return str(exc)
+        return None
+
+
+@pytest.fixture(scope='session')
+def sphinx_remote_query_address() -> tuple[str, int]:
+    """Address to which a query is made to check that the host is online.
+
+    By default, onlineness is tested by querying the DNS server ``1.1.1.1``
+    but users concerned about privacy might change it in ``conftest.py``.
+    """
+    return ('1.1.1.1', 80)
+
+
+@pytest.fixture(scope='session')
+def if_online(  # NoQA: PT004
+    request: pytest.FixtureRequest,
+    sphinx_remote_query_address: tuple[str, int],
+) -> None:
+    """Skip the test if the host has no connection.
+
+    Usage::
+
+        @pytest.mark.usefixtures('if_online')
+        def test_if_host_is_online(): ...
+    """
+    if _HOST_ONLINE_ERROR not in request.session.stash:
+        # do not use setdefault() to avoid creating a socket connection
+        lookup_error = _query(sphinx_remote_query_address)
+        request.session.stash[_HOST_ONLINE_ERROR] = lookup_error
+    if (error := request.session.stash[_HOST_ONLINE_ERROR]) is not None:
+        pytest.skip('host appears to be offline (%s)' % error)
+
+
 @pytest.fixture(scope='session')
 def sphinx_test_tempdir(tmp_path_factory: Any) -> Path:
     """Temporary directory."""
@@ -233,8 +289,8 @@ def rollback_sysmodules() -> Generator[None, None, None]:  # NoQA: PT004
     For example, used in test_ext_autosummary.py to permit unloading the
     target module to clear its cache.
     """
+    sysmodules = list(sys.modules)
     try:
-        sysmodules = list(sys.modules)
         yield
     finally:
         for modname in list(sys.modules):
diff --git a/tests/test_builders/test_build_html_image.py b/tests/test_builders/test_build_html_image.py
index 8c3d309d4..66ba58df0 100644
--- a/tests/test_builders/test_build_html_image.py
+++ b/tests/test_builders/test_build_html_image.py
@@ -5,6 +5,7 @@ import docutils
 import pytest
 
 
+@pytest.mark.usefixtures('if_online')
 @pytest.mark.sphinx('html', testroot='images')
 def test_html_remote_images(app, status, warning):
     app.build(force_all=True)
@@ -24,6 +25,7 @@ def test_html_encoded_image(app, status, warning):
     assert (app.outdir / '_images/img_#1.png').exists()
 
 
+@pytest.mark.usefixtures('if_online')
 @pytest.mark.sphinx('html', testroot='remote-logo')
 def test_html_remote_logo(app, status, warning):
     app.build(force_all=True)
diff --git a/tests/test_builders/test_build_latex.py b/tests/test_builders/test_build_latex.py
index 2c2c3acdc..e9114b5c4 100644
--- a/tests/test_builders/test_build_latex.py
+++ b/tests/test_builders/test_build_latex.py
@@ -1398,6 +1398,7 @@ def test_latex_raw_directive(app, status, warning):
     assert 'LaTeX: abc def ghi' in result
 
 
+@pytest.mark.usefixtures('if_online')
 @pytest.mark.sphinx('latex', testroot='images')
 def test_latex_images(app, status, warning):
     app.build(force_all=True)