The former Chelsea striker was absent from the Saputo Stadium where his side claimed a 2-2 draw to seal a Major League Soccer play-off spot.
Montreal Impact had earlier said the 38-year-old had a back injury to explain his omission from the squad.
Biello however later revealed that he had refused to start on the bench.
“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. The organisation will have to handle this,” the coach added.
Drogba has scored 10 goals in 21 appearances for Montreal this season.