The operation was announced by Devils general manager Lou Lamoriello after New Jersey's 1-0 overtime win against the Buffalo Sabres on Wednesday night.
Rolston has already missed two games after being leaving New Jersey's loss at Washington on Saturday because of groin stiffness.
"It's unfortunate because I thought Brian had a very good training camp," Devils coach John MacLean said. "He had a lot of jump and was playing really well. It's just an unfortunate situation."
Rolston will likely be placed on long-term injured reserve, which will free up $5 million of salary cap space for the Devils, who have played two straight games with a depleted roster. The 16-year NHL veteran scored 20 goals last season -- third-most on the team -- and 37 points in 80 games.