The 37-year-old singer went to a restaurant in Santa Monica, Giorgio Baldi, with his ex-wife Gwyneth Paltrow and their two children, Apple and Moses, when the alleged incident happened.
While leaving the restaurant, a photographer ran to Martin's car and was allegedly struck by his jeep. An ambulance was then called and the photographer was rushed to hospital, reported TMZ online.
"Here is the weird thing. The photographer who took pics of the accident was standing across the street. It's unclear why the cameraman would be so far away, because there was a clear shot of the family from the restaurant side...Right on the sidewalk. In fact, three other photographers were perched right there," the site said.
The site also noted that when the injured photographer was wheeled away by the officer, he looked directly at the other photographer who snapped pics of the incident.
Martin has not yet commented in public regarding to the incident.