diff --git a/python/ray/autoscaler/command_runner.py b/python/ray/autoscaler/command_runner.py
index 1d1602708..1da2f8836 100644
--- a/python/ray/autoscaler/command_runner.py
+++ b/python/ray/autoscaler/command_runner.py
@@ -617,6 +617,10 @@ class DockerCommandRunner(SSHCommandRunner):
             f"mkdir -p {os.path.dirname(target.rstrip('/'))}")
         self.ssh_command_runner.run_rsync_up(source, target)
         if self._check_container_status():
+            if os.path.isdir(source):
+                # Adding a "." means that docker copies the *contents*
+                # Without it, docker copies the source *into* the target
+                target += "/."
             self.ssh_command_runner.run("docker cp {} {}:{}".format(
                 target, self.docker_name,
                 self._docker_expand_user(protected_path)))
@@ -627,6 +631,10 @@ class DockerCommandRunner(SSHCommandRunner):
             source = source.replace("/root", "/tmp/root")
         self.ssh_command_runner.run(
             f"mkdir -p {os.path.dirname(source.rstrip('/'))}")
+        if protected_path[-1] == "/":
+            protected_path += "."
+            # Adding a "." means that docker copies the *contents*
+            # Without it, docker copies the source *into* the target
         self.ssh_command_runner.run("docker cp {}:{} {}".format(
             self.docker_name, self._docker_expand_user(protected_path),
             source))