Jacquet fell awkwardly in the second half of the French league match and appeared in agony as he left the pitch.
"For Jeremy, it's his shoulder, and for Abdelhamid (Ait Boudlal, another Rennes player injured in the same match) it's muscular," Rennes head coach Habib Beye told reporters after the match.
"We'll have time to see, but it's definitely quite serious for both of them."
Liverpool agreed a 60-million-pound ($80-million) deal for Jacquet on Monday, but the 20-year-old defender will stay with the French club until the end of the season.
Liverpool, provisionally sixth in the Premier League table, will face Manchester City on Sunday with four defenders - Giovanni Leoni, Joe Gomez, Jeremie Frimpong and Conor Bradley - sidelined due to injuries.