It was initially feared that Godwin would be highly unlikely to play again this season.
The in-form hooker damaged a knee during Warriors' last-gasp 34-28 defeat to Wakefield Trinity Wildcats at the JJB Stadium on Friday, the diagnosis being cartiledge damage which is expected to keep him out for a minimum of 3 weeks meaning he is likely to play before the end of the season.
Godwin was unable to go back on and relieve his tiring team-mates during a sapping second half and was sent to hospital at the end of the match.
Meanwhile young full-back Chris Melling is also on crutches with a knee injury he received against St Helens a fortnight ago.
He needs an operation and is unlikely to figure again this season.
It is the second time in two years Melling has suffered a bad knee injury.
He was carried off at Headingley at the start of last season and missed an entire summer of rugby league.
Chairman Maurice Lindsay said:
"This year, it seems as though there's been some devastating news on the injury front after every game.
"Starting with Luke Davico in a pre-season friendly, the players have been dropping like flies.
"It is a great shame for Wagga because the lad's been in cracking form.
"And the same goes for poor Chris who is also hobbling about the place on crutches.
"To pick up yet more serious injuries at this stage of the season after what we've been through already is just unbelievable.
"It's been a horrible season for us on the medical front.
"I don't particularly wish bad luck on other rugby league clubs, but surely it has to be somebody else's turn soon?"
The Wigan team now have two weeks off before the next game which is at home against Salford City Reds on Friday, August 5.