The 38-year-old, who has 46 club appearances this term, sustained an apparent knock to his shoulder during Denmark’s Nations League quarter-final second-leg defeat in Portugal last month.
The Denmark veteran, who has 81 caps, played on in the 5-2 loss that meant the Portuguese progressed 5-3 on aggregate.
Asked about the likely five-to-six-week absence, Rodgers told Celtic TV: “This is just something that, day by day, we’ll have a look at, but the timeline that was given to us was maybe around about that.
“Kasper tends to think it might not be as long as that, but certainly in the immediate future he won’t be available.”Viljami Sinisalo deputised for Schmeichel in Saturday’s 3-0 Scottish Premiership win over Heart of Midlothian – the 23-year-old Finn’s second Celtic appearance.
Rodgers’ side visit St Johnstone in the league on Sunday, then host Kilmarnock on 12 April, before the Scottish Cup holders meet Saints in their semi-final at Hampden Park on 20 April.
After that, the defending league champions will have five more Premiership games against top-six sides and possibly a Scottish Cup final versus Aberdeen or Hearts to play.
