The incident was reported about 2 p.m. Friday and took place outside the lower level of the Tom Bradley terminal, police said.
A scuffle took place after a photographer continued to take pictures of the rapper after being told that West did not want his picture taken, sources familiar with the investigation said.
Paramedics were called to the scene after the paparazzo complained of injuries. Sources said there were no immediate or visible signs of injury.
West left the area before police arrived.
Police officials said the photographer was knocked to the ground during the incident but did not specify how that occurred.
The investigation is being handled by LAPD's Pacific Division.
Samir Chantre, a Brazilian jiujitsu instructor who was returning from a flight from Brazil at the time, said in a telephone interview with The Times that the incident occurred about 2 p.m. outside the international terminal.
When West exited the airport, Chantre said, "five photographers started shooting pictures of him and one of them was over the microphone and was saying stuff to him," Chantre said.
According to Chantre, West "seemed like he was getting offended" and eventually ran after one of the photographers.
Chantre said the two were pulled apart by onlookers.