FIFA says its disciplinary committee will examine charges of "unsporting behaviour" against Sinclair.
Canada lost a dramatic semifinal 4-3 on Aug. 6, with the eventual Olympic champions scoring the winner late in extra time.
Sinclair, whose hat trick gave Canada the lead three times, was quoted saying the team felt "cheated."
Canada's players were angered that Norwegian referee Christiana Pedersen penalized goalkeeper Erin McLeod for holding the ball too long in the 80th minute.
The free kick led to a penalty which U.S. forward Abby Wambach scored to send the match into extra time.