Boateng left Munich on Monday to be with his son in Leipzig without permission from his club.
The 31-year-old then crashed his Mercedes car on his way back to the City.
The city of Bavaria is on government lockdown as Germany try to stifle the spread of Covid-19, which has seen 84,794 cases and 1,107 deaths recorded in the country.
A statement from the German champions read: "Boateng has transgressed the guidelines issued by the club by being too far away from his home.
"These guidelines govern the behaviour of the FC Bayern players in the current situation in line with the Bavarian state government's directives on restrictions on movement and the recommendations of the health authorities.
"FC Bayern believes the club has a responsibility to be a role model. As a consequence of this transgression, the club has decided to impose a fine on Boateng. The club will donate the money to Munich hospitals."
Boateng has accepted responsibility for his actions but feels the club should have been merciful in the prevailing circumstances.
"I know that it was certainly a mistake not to inform the club about my trip, but in the moment I only had my son in mind,” the World Cup winner told Bild.
“He was not in good health. When a son calls his father, of course I will still go, no matter what time!
“For him I accept any punishment; after all, he is my son.
“I want to see the father who does not go in such a moment to be with his four-year-old son. If there is a punishment for it, then I respect it. I find it sad.”
