Both forwards were injured in Winnipeg's 5-4 shootout win over Edmonton on Monday.
Coach Paul Maurice said Perreault had a "significant lower-body injury."
"We would be hopeful that he'll return by the end of the regular season," Maurice said after practice on Wednesday. "If he does, it won't be much sooner than that."
That means Winnipeg will have to continue its playoff push without Perreault, a key forward. The Jets entered Wednesday's games in contention for a playoff spot in the Western Conference.
Maurice said Stafford is day-to-day with an upper-body injury and will skate before Winnipeg's game in Washington on Thursday.