Pierce will miss at least one game with an injured left foot, the Blue Bombers confirmed Sunday.
"He'll be out this week, we'll have better information in the next day or so for how long," Winnipeg head coach Paul LaPolice said to media at practice.
Backup QB Alex Brink will get the start on Wednesday against the Argonauts in Toronto.
Pierce left Friday's 42-10 loss to the Eskimos in the first quarter after being sacked by Edmonton's Ted Laurent.
The 30-year-old import missed 13 games due to injury in the 2010 season and two games in 2011.
Brink is also banged up. He left Winnipeg's loss to the Eskimos in the fourth after having his bell rung by J.C. Sherritt, leaving the Bombers offence in the hands of Joey Elliott.
However, Brink feels ready to play in Toronto.
"I'll be good to go on Wednesday," Brink told media on Saturday. "I don't have a headache, I have full memory of everything that happened."
Elliott will back up Brink against the Argonauts.
LaPolice was unsure if Pierce would return for July 26, when the Bombers host Edmonton.
"The biggest thing is evaluating Buck and seeing where he's at," said LaPolice on Saturday. "He was pretty sore this morning, in a lot of pain."
Pierce has thrown for 327 yards in three games this season, completing 24 of 40 passing attempts. He's scored a touchdown and has been intercepted three times. Pierce has also rushed eight times for 41 yards.
Brink has thrown for 253 yards in 2012, completing 25 of 48 passes with two TDs and two interceptions.
He's rushed for 28 yards on six carries, scoring one touchdown.