Former Hammers midfielder Frank Lampard scored his 200th goal for the Blues to open the scoring and celebrated in front of the away fans as missiles flew onto the pitch.
A Met Police spokesperson said: "We are investigating instances of coin-throwing at Chelsea versus West Ham on Sunday, March 17. There have been no arrests. Inquiries continue."
West Ham issued a statement that said that they would assist Chelsea in the investigation and possibly ban any individual found guilty.