The midfielder sustained the injury during training with the Light Blues in Germany on Thursday and is expected to be sidelined for several weeks.
Hutton was stretchered off the pitch after falling to the turf with no other player around him and was immediately taken to hospital for an X-ray.
His injury follows a similar problem suffered by Ross Perry earlier this month, with the defender set to miss the start of the season.
Speaking about Hutton, 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 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."