Numerous witnesses were interviewed about the afternoon incident to compile a report for detectives to investigate, LAX Police Sgt. Steve Savala said.
Video shows West being thronged by cameras while trying to get into a white Mercedes Benz waiting curbside.
As flashbulbs illuminate his face, West accuses the paparazzi of trying to provoke him "so I have to pay you, like, $250,000." He then lunges at a photographer's camera and tries to wrestle it away.
West has had similar run-ins with paparazzi at LAX before, trading barbs with photographers who follow his every move.
The rapper's critically acclaimed album "Yeezus" debuted at No. 1 on the Billboard 200 charts last month, but sales have dropped off in weeks since. West's other recent debut - his daughter, North, with reality television star Kim Kardashian - turned 1 month old this week.