Speaking exclusively to Football Insider, the former Rangers defender insisted Ange Postecoglou will be “gutted” to lose the 28-year-old for a couple of weeks.
As quoted by BBC Sport, Postecoglou confirmed Rogic will be out of action for Celtic until after the international break.
The Australia international picked up the hamstring issue in the 3-1 win over Hibernian.
He sat out the Bhoys’ 0-0 draw against Livingston on Saturday.
Hutton insisted Rogic has looked back to his best since Postecoglou took charge this summer.
As such, he insisted the Hoops will want him back as soon as possible.
Hutton told Football Insider’s Russell Edge: “Postecoglou will be gutted.
“When he came in, I thought he could get the best out of Rogic. I always thought he was a fantastic player who then went off the boil a little.
“His performances over the past few weeks have been of a high level. I thought Celtic were excellent against Hibs, which was a tough game. Rogic was a big part of that.
“Obviously to lose him is very disappointing because it was hitting those heights he was at a few seasons ago. He was a constant thorn in Rangers’ side every time he played them.
“He was getting back to that. So he’ll be hoping that he’s not out for too long because he’ll be a huge miss and they’ll need him.”
Celtic face Ferencvaros and Dundee before the international break.