He had skated Monday with goaltending coach Stephane Waite for approximately 40 minutes before leaving the ice as the Canadiens were about to begin practice. He also worked out off the ice with teammates prior to practice.
"He's obviously doing better than he was doing before, but this is just one step," Therrien said. "He came to work out [Sunday] a bit here in the gym, and as you saw he got back on the ice [Monday], which is good news. He's going in the right direction, which is encouraging news."
Price missed Montreal's first two games of the regular season, a 4-1 win at the Buffalo Sabres on Thursday and a 4-3 shootout loss at the Ottawa Senators on Saturday.
Montoya is 1-0-1 with a 1.92 goals against average and a .942 save percentage.
"He's been great," Canadiens defenseman Shea Weber said. "I think you guys have seen how good he's been. He's been real solid for us. Obviously it's a nice guy to have back there when Price is not feeling so well, a guy that can step up and do the job that he's done."
Price last was on the ice Oct. 9. The Canadiens announced Oct. 14 that Price had the flu with a fever, and that he was taking antibiotics and was being evaluated by team physician Dr. David Mulder.
The last game Price played for the Canadiens was Nov. 25, 2015, when he sustained a season-ending sprain of the medial collateral ligament in his right knee. Price started last month for Team Canada in its run to the championship of the World Cup of Hockey 2016.