The former Chelsea striker, 38, was accused of refusing to play against Toronto on Sunday.
Impact coach Mauro Biello suggested Drogba had reacted badly after being told he would not start the game.
“We met with Didier. The situation has been resolved to the club’s satisfaction,” Saputo said.
“Didier has accepted to assume the role that the head coach sees fit while contributing to the success of this club moving forward.”
Drogba was absent from the Saputo Stadium on Sunday, when the Impact claimed a 2-2 draw to seal a Major League Soccer play-off spot.
Montreal had initially explained his omission by saying he had a back injury.
But Biello said after the match: “He didn’t accept that he would come off the bench and, in the end, he didn’t want to be in the 18.
“There was tightness in his back, yes, but he was capable of playing.”
Drogba, who left Chelsea in July 2015, has been used as a substitute in two of the Impact’s past four games.
The former Ivory Coast international has scored 10 goals in 21 appearances this season.