Coan, facing his former team at Soldier Field, limped off after Notre Dame's second possession of the third quarter with the score tied 10-10. After a quick visit to the medical tent, he was taken to the locker room.
Kelly said X-rays were "clean" and Coan's injury doesn't appear serious.
"It's a soft-tissue injury," Kelly said. "It doesn't even respond like a high ankle sprain, so we're pretty optimistic that we'll be able to see him back next week."
The No. 12 Fighting Irish (4-0) host Cincinnati on Oct. 2.
Against the Badgers, Notre Dame fell behind 13-10 before scoring 31 unanswered points in the final 14:01 -- starting with a 96-yard kick return touchdown by Chris Tyree -- as Kelly surpassed Knute Rockne to become the school's all-time coaching wins leader with 106.
With true freshman Tyler Buchner, who played briefly in the past two games, unavailable due to a hamstring injury, second-year quarterback Drew Pyne replaced Coan and passed for 81 yards and a touchdown.
Kelly praised Pyne, who chose to remain with Notre Dame even after Coan transferred from Wisconsin, but the coach emphasized Coan will be the starter when he is healthy enough to play. Buchner also likely will return next week, Kelly said.
The Irish remain an evolving team dealing with inexperience and attrition at certain spots, Kelly said, but the coach loves the group's approach to preparation. The Irish's defense, which struggled in wins over Florida State and Toledo, stopped the Badgers on 13 of 14 third-down conversion attempts, including the first 10.
Notre Dame had only 60 yards in the fourth quarter but became just the second FBS team in the past 15 years to erase a deficit in the final quarter to win by 28 points or more.
"It's one thing to practice, but you got to flip it to a performance mindset," Kelly said. "They can flip it. They can prepare and then flip it to performance, and that's a really good thing to do. ... We've got a long way to go still, but they're getting better each week. I'm having fun coaching them.
"They're not perfect by any means, but they're going to be better in November, and that's the nice part about it. That's what energizes you as a coach."
Kelly began his postgame news conference by apologizing for his "sticky Gatorade haircut," as players doused him after the game. Now in his 12th season, Kelly is 106-39 at Notre Dame with two CFP appearances and a BCS title game appearance in 2012.
"I'm just glad it's over with," Kelly said of eclipsing Rockne's record. "I'm proud of the accomplishment to the level of consistency, and obviously, from a winning standpoint, you have to have great players and great coaches and great support. ... But I get more joy in watching the development of a Drew Pyne going in there and Chris Tyree. That's why I do this. You don't do it for 31 years because you're trying to beat Knute Rockne's record.
"I mean no disrespect to Knute, but I'm just glad it's over with, and we can move on to trying to beat Cincinnati."
There is a caveat, however, as the NCAA ordered the Irish to vacate 21 victories from the 2012 and 2013 seasons as part of sanctions related to academic misconduct. The NCAA denied an appeal in February 2018. So, as far as the NCAA is concerned, Kelly's record stands at 85-39 in 12 seasons.
Notre Dame QB Jack Coan limps off field in third quarter
Notre Dame's Jack Coan limps off the field after passing the ball in the third quarter.
ND capitalizes on INT as Coan drops dime to Austin for TD
Cam Hart picks off the Graham Mertz pass setting up a Jack Coan toss to Kevin Austin Jr. for the 36-yard touchdown.