The 22-year-old was stretchered off the pitch at the Klosterpforte Hotel having fallen to the turf with no other player around him.
Hutton, who has made 47 appearances scoring twice for the third division champions, sustained a similar problem to Ross Perry, with the defender set to also miss the start of the season.
Hutton tweeted: "Gutted about my injury couldn't have came at a worse time but it comes with the job just need to get on with it and get back fit again!"
Speaking about his team-mate, skipper Lee McCulloch told the club's website: "Over the close season I trained a wee bit with him as he wanted to be a lot fitter than he was last season.
"He got himself in peak condition and in pre-season so far he's probably been our best player.
"He did well last season but I think he's raised the bar since he has come in for this pre-season.
"Having been running with him and doing little bits of training with him this summer you could see he was getting a bit of shape to his body and really looking good.
"We all feel for him right now but hopefully he will be back soon and he can kick on again."
Meanwhile, Rangers also confirmed they have reached a "mutual agreement" with Francisco Sandaza to end his employment with the club.
The Light Blues announced in April they had terminated the striker's contract following an investigation into a hoax phone call, with reports at the time suggesting the Spaniard was set to appeal against the decision.
A statement on the club's website read: "The club can confirm that we have reached a mutual agreement with Fran Sandaza to terminate his contract."