The Italian 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 not had much luck with injuries after arriving in the summer from Roma, having missed three months after breaking a foot in October.
"It's unfortunate. It's actually the other shoulder to a similar injury he had when he was at Chelsea," Rodgers told the post-match press conference.
"It looks like in the early stages that (dislocated shoulder) is the diagnosis."