diff --git a/tools/install/bazel/drake.BUILD.bazel b/tools/install/bazel/drake.BUILD.bazel
index 01b3ccf83a2d..988474b2be39 100644
--- a/tools/install/bazel/drake.BUILD.bazel
+++ b/tools/install/bazel/drake.BUILD.bazel
@@ -7,6 +7,8 @@ package(default_visibility = ["//:__subpackages__"])
 
 _DRAKE_RUNFILES = MANIFEST["runfiles"]["drake"]
 
+_PYTHON_SITE_PACKAGES_RELPATH = MANIFEST["python_site_packages_relpath"]
+
 _DRAKE_ROOT_PACKAGE_RUNFILES = [x for x in _DRAKE_RUNFILES if "/" not in x]
 
 _EXPECTED_DRAKE_RUNFILES_PACKAGES = [
@@ -55,7 +57,16 @@ filegroup(
     ]),
 )
 
-_IMPORT = ".lib/python3.6/site-packages"
+_IMPORT = "." + _PYTHON_SITE_PACKAGES_RELPATH
+
+# N.B. This is not a standalone Python library.
+# TODO(eric.cousineau): Expose this as an alias
+# `@drake//lcmtypes:lcmtypes_drake_py` when it can only depend on specific
+# parts of the runfiles (not all of pydrake).
+py_library(
+    name = ".lcmtypes_drake_py",
+    srcs = glob(["*.py"]),
+)
 
 py_library(
     name = ".pydrake",
@@ -68,6 +79,9 @@ py_library(
         ":.all_runfiles",
         ":.drake_shared_library",
     ],
+    deps = [
+        ":.lcmtypes_drake_py",
+    ],
     imports = [
         _IMPORT,
     ],
diff --git a/tools/install/bazel/generate_installed_files_manifest.bzl b/tools/install/bazel/generate_installed_files_manifest.bzl
index 2f216db40f6a..6c637859073c 100644
--- a/tools/install/bazel/generate_installed_files_manifest.bzl
+++ b/tools/install/bazel/generate_installed_files_manifest.bzl
@@ -2,6 +2,7 @@
 # vi: set ft=python :
 
 load("@drake//tools/install:install.bzl", "InstallInfo")
+load("@python//:version.bzl", "PYTHON_SITE_PACKAGES_RELPATH")
 
 def _impl(ctx):
     known_non_runfiles = [
@@ -13,18 +14,24 @@ def _impl(ctx):
         "setup/requirements.txt",
     ]
     drake_runfiles = []
+    drake_prologue = "share/drake/"
+    lcmtypes_drake_py_files = []
+    lcmtypes_drake_py_prologue = PYTHON_SITE_PACKAGES_RELPATH + "/drake/"
     for dest in ctx.attr.target[InstallInfo].installed_files:
-        prologue = "share/drake/"
-        if not dest.startswith(prologue):
-            continue
-        drake_relative_path = dest[len(prologue):]
-        if drake_relative_path in known_non_runfiles:
-            continue
-        drake_runfiles.append(drake_relative_path)
+        if dest.startswith(drake_prologue):
+            relative_path = dest[len(drake_prologue):]
+            if relative_path in known_non_runfiles:
+                continue
+            drake_runfiles.append(relative_path)
+        elif dest.startswith(lcmtypes_drake_py_prologue):
+            relative_path = dest[len(lcmtypes_drake_py_prologue):]
+            lcmtypes_drake_py_files.append(relative_path)
     content = {
         "runfiles": {
             "drake": sorted(drake_runfiles),
         },
+        "lcmtypes_drake_py": sorted(lcmtypes_drake_py_files),
+        "python_site_packages_relpath": PYTHON_SITE_PACKAGES_RELPATH,
     }
     ctx.actions.write(
         output = ctx.outputs.out,
diff --git a/tools/install/bazel/repo_template.bzl b/tools/install/bazel/repo_template.bzl
index 49be67385cc5..e72e12858b90 100644
--- a/tools/install/bazel/repo_template.bzl
+++ b/tools/install/bazel/repo_template.bzl
@@ -79,6 +79,16 @@ def _drake_impl(repo_ctx):
     for relpath in _MANIFEST["runfiles"]["drake"]:
         repo_ctx.symlink(str(share_drake) + "/" + relpath, relpath)
 
+    # Symlink all drake LCM types to this repository's root package, since it
+    # should be named `drake` (see bazelbuild/bazel#3998).
+    if repo_ctx.name != "drake":
+        print("WARNING: Drake LCM types will not be importable via `drake` " +
+              "if this repository is not named `drake`.")
+    python_site_packages_relpath = _MANIFEST["python_site_packages_relpath"]
+    drake_lcmtypes_package = "." + python_site_packages_relpath + "/drake"
+    for relpath in _MANIFEST["lcmtypes_drake_py"]:
+        repo_ctx.symlink(drake_lcmtypes_package + "/" + relpath, relpath)
+
     # Emit the manifest for later loading.
     manifest_bzl = "MANIFEST = " + struct(**_MANIFEST).to_json()
     repo_ctx.file(".manifest.bzl", content = manifest_bzl, executable = False)
diff --git a/tools/install/bazel/test/drake_bazel_installed_test.py b/tools/install/bazel/test/drake_bazel_installed_test.py
index 1dff3e0d9670..37ee423240d9 100644
--- a/tools/install/bazel/test/drake_bazel_installed_test.py
+++ b/tools/install/bazel/test/drake_bazel_installed_test.py
@@ -37,6 +37,13 @@ def main():
     deps = ["@drake//bindings/pydrake"],
 )
 
+py_test(
+    name = "import_all_test",
+    srcs = ["import_all_test.py"],
+    size = "small",
+    deps = ["@drake//bindings/pydrake"],
+)
+
 # A stub for unit testing; not required for end users.
 filegroup(name = "dummy_filegroup")
 """)
@@ -46,6 +53,11 @@ def main():
 from pydrake.common import FindResourceOrThrow, set_log_level
 set_log_level("trace")
 FindResourceOrThrow("drake/examples/pendulum/Pendulum.urdf")
+""")
+
+    with open(join(scratch_dir, "import_all_test.py"), "w") as f:
+        f.write(f"""
+import pydrake.all
 """)
 
     # Check that a full `bazel test` passes.