The following definition is from dictionary.com:
Do someone (or somebody) wrong => do someone damage or harm. Injure someone; be unfaithful or disloyal; act unjustly or unfairly toward someone. For example, John's done me wrong, and I intend to tell him so, or She did him real damage when she started that rumor: The first term dates from the late 1300s; the substitutions of damage and harm are newer. However, while these locutions are still current, a more common modern usage is to turn them into verbal phrases that is, wrong someone, harm someone, damage someone.