Bajcetic suffered the injury in training earlier this week and missed Wednesday's 1-0 defeat to Real Madrid in the UEFA Champions League as a result.
The 18-year-old Spaniard has enjoyed a breakthrough season for Liverpool this season, making 19 appearances across all competitions and scoring his first senior goal against Aston Villa in the Premier League back in December.
“Unfortunately I’ve picked up an injury that will keep me out until the end of the season,” Bajcetic wrote on Instagram.
“It’s very sad to say goodbye to this amazing season for me but I understand this is part of football and will only make me stronger physically and mentally.
“I would also like to say thank you to you reds for all the support through the season and I assure you I will do my best to be back stronger than ever.”
Bajcetic was rewarded with a new contract until 2027 by Liverpool in January.
He joined the club from Celta Vigo in December 2020.