The 25-year-old has played six games for the Lions since joining from Reading last month, helping the club to clean sheets in half of those games.
"Shaun has been complaining of a sore groin but has been putting himself up to play," News at Den quotes Millwall boss Ian Holloway as saying.
"We sent him for a scan yesterday and there's a tear in one of his muscles in the groin. It's a very important muscle and if that goes, it will rupture. We can't risk him for at least four weeks.
"It's not good news but this will give someone else a chance to play."
Millwall are a point from safety in the bottom three and next host fellow Londoners Fulham on Saturday.