Drogba refused to play for Montreal Impact after being told he would not be starting against Toronto, according to coach Mauro Biello.
The ex-Chelsea striker, 38, was absent from the Saputo Stadium where the Impact claimed a 2-2 draw to seal a Major League Soccer play-off spot.
Biello said: "He didn't accept that he would come off the bench and, in the end, he didn't want to be in the 18."
The coach added: "There was tightness in his back, yes, but he was capable of playing. The organisation will have to handle this."