Sabres coach Lindy Ruff refused to give a specific timetable on how long the speedy forward would be sidelined, other than saying it would be "a while."
Afinogenov was hurt after being checked into the boards by Toronto defenceman Wade Belak. He played five shifts, totalling nearly four minutes, before heading to the dressing room. He didn't return.
Afinogenov, with eight goals and 11 assists, entered the night tied with Atlanta's Marian Hossa for second in scoring in the NHL. He had points in nine of Buffalo's first 13 contests and was on a three-game scoring streak before Saturday's loss to the Maple Leafs.
The Sabres recently lost Henrik Tallinder, one of their top defencemen, for six weeks because of a broken left forearm.
"We have to fight through these adversities," Sabres centre Derek Roy said. "We need to bear down and play our game."
Afinogenov led the Sabres last season with a career-high 73 points, including 51 assists. He missed five games in November because of bruised ribs.