The 34-year-old actor allegedly tried to grab the photographer's camera during the incident on Tuesday, Britain's Press Association said. He was released on bail and must return to a London police station in October.
Law's publicist was not immediately available for comment.
Police would not directly confirm the report, but said a 34-year-old man from Law's neighborhood was arrested on suspicion of causing bodily harm. Police added the man voluntarily went to a police station for questioning.