"It's not something that's displaced or out of whack,'' Quinn said of Coleman's injury. "So, I'm not going to put a timetable on it until we know how he's responding to it. And then as we get later in the week, then we can put more of a timetable on it.''
Coleman's return depends on his pain threshold, Quinn said.
"His first time going through it, so that's why we don't want to put like a distance on it at this point,'' the coach said.
While Quinn wouldn't put a time frame on Coleman's absence, a source told ESPN's Adam Schefter that the running back is expected to miss a couple of weeks.
Quinn said he does not anticipate signing another running back at this time.
Coleman will sit out practices Wednesday and Thursday of this week, Quinn said.
Coleman, who won the starting job going into the season ahead of second-year player Devonta Freeman, scored his first career touchdown on a 1-yard run in the first quarter of Sunday's victory over the New York Giants.
He had nine rushes for 32 yards before being carted off in the second quarter.
With Coleman out, Freeman will take over the carries in the backfield with undrafted rookie Terron Ward behind him.
In other news, Quinn said starting middle linebacker Paul Worrilow suffered a bruised right calf during Sunday's win over the Giants and is day-to-day. Worrilow did not need to undergo an MRI.
ESPN.com's Vaughn McClure contributed to this report.