The 30-year-old defender suffered the problem in a tackle on David Mooney two minutes after he had opened the scoring with his first goal of the season.
Boss Brendan Rodgers is fearing the worst for Monk, who could miss the rest of the season.
"It isn't looking too good for Garry and we've sent him home to gather his thoughts ahead of a scan on his knee on Sunday," said Rodgers.
"I'm gutted for him because he had just scored his first goal of the season. Losing him for a period of time will be a big blow for us.
"He has had a bad injury on that knee before and he could be out for the rest of the season. That would be a massive blow for us because he has been a fantastic leader both on and off the field all season."