"We are investigating instances of coin-throwing at Chelsea versus West Ham. There have been no arrests. Inquiries continue," said a Met police spokesman on Monday.
Lampard, who joined Chelsea from West Ham in 2001, headed in the game's opener after 19 minutes at Stamford Bridge and the goal was greeted with abuse from the nearby away fans who threw coins and hot dogs.
The England international's strike was his 200th for the European champions as he closes in on the club record of 202 set by Bobby Tambling in the 1960s and 1970s.
Two men were also arrested due to alleged racially-aggravated public order offences, police have announced.
The two men have been bailed to return to later this month.
The Football Association said it will liaise with the police and the two clubs involved.