He is accused of receiving money from the boss of a giant meatpacking firm implicated in a corruption scandal. Mr Temer denies any wrongdoing.
The charges have been delivered to a Supreme Court judge who must now decide if the case can be sent to the lower house of parliament.
The lower house would then vote on whether President Temer can be tried.
Mr Temer has vowed to prove his innocence. He has faced a slew of accusations since taking office last year but these are the first formal charges against him.
The move follows the release of an audio recording in which Mr Temer appears to be discussing bribes in conversation with Joesley Batista, the chairman of the meatpacking company JBS.
President Temer is expected to face further charges in the coming weeks, correspondents say.
He is deeply unpopular in Brazil but his centre-right party has been able to govern as part of a coalition.
Opposition parties have been demanding snap elections and his impeachment.
Photo: AFP Brazilian President Michel Temer has faced a slew of accusations since taking office last year.