The Italian striker, who joined the Reds during the summer from Roma, suffered the problem during his side's 5-0 win over Swansea City at Anfield this afternoon.
"It looks like Fabio Borini has a dislocated shoulder which will keep him out for the season. He did a similar one at Chelsea on the other side. It's a big blow for us," Rodgers told BBC Sport.
Borini had only recently returned to the Liverpool squad following a spell on the sidelines with a broken foot.