Celebrity website TMZ said Bieber motioned the photographers to clear out of the way but apparently pinned one between his Ferrari and a parked car as he pulled out. He then drove away.
"It was not a hit-and-run," Los Angeles Police Department spokesman Bruce Borihanh said on Tuesday. "The investigation is ongoing."
He said the photographer's injuries were not life-threatening.
A representative for Bieber declined to comment.
Bieber is under investigation in a separate driving incident in May after his neighbors complained that he had been speeding through his gated Los Angeles-area community.
The Canadian singer has been the subject of a series of headline-grabbing incidents over the past year. German authorities seized a capuchin monkey Bieber had kept as a pet after he was unable to provide proper documentation for the animal at Munich airport. And in London, the singer scuffled with a photographer outside a hotel during a European tour.