The Scottish winger is currently laid low with the injury and reports indicate he will miss a few pre-season games and even the kick off to the campaign.
McGovern was one of Wednesday's best players in their promotion season and his loss at the start of the season would leave Paul Sturrock a massive selection dilemma.
In other news, The Owls have re-signed Chris Adamson to be the club's back-up goalkeeper behind David Lucas.
Adamson came on for Lucas in the win against Blackpool and deputised for him at Colchester the following week before Paul Gallacher came in from Norwich.