The injury occurred at the end of the first quarter on a 61-yard catch as Evans was racing past Pierre Desir for a touchdown. Evans attempted to walk off the injury before collapsing in pain in the end zone.
After the game, coach Bruce Arians said Evans' prognosis was "not good" and "he'd be shocked" if the Pro Bowl receiver made it back before the end of the season.
On Monday, Arians was cautiously optimistic.
"They're going to let it bleed out. He was a quick healer when he had it in the spring," Arians said. "I would be very doubtful for this week."
Justin Watson, who caught a 17-yard touchdown Sunday in the first significant action of his career, is expected to take Evans' spot.
Evans has 67 catches this season and is third in the NFL with 1,157 receiving yards. He has scored eight touchdowns, and his average of 17.3 yards per catch ranks sixth in the league.
Evans has missed three games during his six-year career and has never missed more than one game per season.
Last month, Evans joined Hall of Famer Randy Moss as the only players in NFL history to reach 1,000 receiving yards in each of their first six seasons.