After suffering a broken nose on Saturday, the former Hull man was told he would need splints in order to help his breathing and prevent long spells of bleeding.
The news of the delay on op has come as good news to Groves who would surely need to loan a defender if Edwards was out for the suggested three weeks.
"He's been told that he needs something doing on it at some stage but it will mean doing nothing for two or three weeks," Groves told the Grimsby Telegraph.
"Maybe if there's a break in the games he might have it done, or it might be the end of the season.
"He joined in with training a little bit yesterday. He's okay mentally and physically, the problem will be if he gets another bang on it and it won't stop bleeding.
"He didn't come off against Colchester because of the broken nose, it was just because of the bleeding."