The Italy international came on as a late substitute but fell awkwardly soon after, with his screams audible from the stands.
Borini immediately came off and went straight down the tunnel as Liverpool finished the match with 10 men.
"It looks like Fabio Borini has dislocated his shoulder, so that would put him out for the rest of the season," manager Brendan Rodgers told BBC Sport.
Borini has had a wretched start to life at Anfield, having also broken his foot earlier this season since joining from Roma for £10.5m in the summer.
The former Chelsea and Swansea forward has only made 16 appearances in all competitions this campaign, scoring once in the Europa League.