The 32-year-old has been playing through the pain barrier for some time, according to Marsh, after completing every minute of the Reds' Premier League season thus far - but Gerrard is now expected to miss England's friendly double-header against Republic of Ireland on May 29 and Brazil in Rio de Janeiro four days later.
|7/1||Steven Gerrard is 7/1 with Coral to open the scoring v Newcastle
"It's looking more and more likely that he might require surgery," Marsh told the club's official website. "He has been playing with a shoulder injury for quite a while now. If it gets to the stage where he gets any worse, we'll try to find the right time for him to get it fixed properly.
"It's not ideal timing, it's going to take quite a while for him to heal. It's a funny injury - it's pretty similar to Joe Allen.
"If it needs repairing, it needs repairing and when he's back fit, he's back fit. There's not much we can do about it."
Gerrard has scored nine Premier League goals this season, plus a further nine assists, as Liverpool look for a Europa League qualification spot before the end of the campaign.