A medical device safety support apparatus features a clamp member configured to be attached to an IV pole, a bed rail, or other support structure. A medical device support member extends from the clamp member and is configured to support a cooperatively configured medical device. The medical device support member may include a socket which receives a post that extends from the medical device, and a lockdown member having a set-screw portion and a handle is provided to secure the post within the socket. The post has a circumferential channel in which the set-screw portion seats, thereby allowing the post to be retained within the socket when the lockdown member is loosened so as to prevent the medical device from being removed from the support member.