diff --git a/internal/fetchdatasource/fetchdatasource_test.go b/internal/fetchdatasource/fetchdatasource_test.go
index 8f93105..d913ad7 100644
--- a/internal/fetchdatasource/fetchdatasource_test.go
+++ b/internal/fetchdatasource/fetchdatasource_test.go
@@ -25,6 +25,7 @@
 	"golang.org/x/pkgsite/internal/proxy/proxytest"
 	"golang.org/x/pkgsite/internal/source"
 	"golang.org/x/pkgsite/internal/stdlib"
+	"golang.org/x/pkgsite/internal/testenv"
 	"golang.org/x/pkgsite/internal/testing/testhelper"
 	"golang.org/x/pkgsite/internal/version"
 )
@@ -428,6 +429,11 @@
 		},
 	} {
 		t.Run(test.path, func(t *testing.T) {
+			if test.modulePath == stdlib.ModulePath {
+				// FetchModule for the stdlib calls stdlib.Versions which makes a network
+				// call to go.googlesource.com for the Go git repo.
+				testenv.MustHaveExternalNetwork(t)
+			}
 			got, err := ds.GetUnitMeta(ctx, test.path, test.modulePath, fetch.LocalVersion)
 			if test.wantErr != nil {
 				if !errors.Is(err, test.wantErr) {
diff --git a/internal/stdlib/stdlib_test.go b/internal/stdlib/stdlib_test.go
index 7297582..8841b0a 100644
--- a/internal/stdlib/stdlib_test.go
+++ b/internal/stdlib/stdlib_test.go
@@ -12,6 +12,7 @@
 	"testing"
 
 	"golang.org/x/mod/semver"
+	"golang.org/x/pkgsite/internal/testenv"
 	"golang.org/x/pkgsite/internal/version"
 )
 
@@ -379,6 +380,8 @@
 }
 
 func TestResolveSupportedBranches(t *testing.T) {
+	testenv.MustHaveExternalNetwork(t) // ResolveSupportedBranches accesses the go repo at go.googlesource.com
+
 	got, err := ResolveSupportedBranches()
 	if err != nil {
 		t.Fatal(err)
diff --git a/internal/testenv/testenv.go b/internal/testenv/testenv.go
new file mode 100644
index 0000000..87dca56
--- /dev/null
+++ b/internal/testenv/testenv.go
@@ -0,0 +1,30 @@
+// Copyright 2023 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package testenv provides information about what functionality
+// is available in different testing environments run by the Go team.
+//
+// It is an internal package because these details are specific
+// to the Go team's test setup (on build.golang.org) and not
+// fundamental to tests in general.
+package testenv
+
+import (
+	"runtime"
+	"testing"
+)
+
+// MustHaveExternalNetwork checks that the current system can use
+// external (non-localhost) networks.
+// If not, MustHaveExternalNetwork calls t.Skip with an explanation.
+func MustHaveExternalNetwork(t testing.TB) {
+	if runtime.GOOS == "js" || runtime.GOOS == "wasip1" {
+		t.Helper()
+		t.Skipf("skipping test: no external network on %s", runtime.GOOS)
+	}
+	if testing.Short() {
+		t.Helper()
+		t.Skipf("skipping test: no external network in -short mode")
+	}
+}