Mike Chappell of Indy Sports Central tweeted that trainers were "being VERY careful" placing him on a cart and "keeping him very still."
Jason La Canfora of CBS Sports noted Williams has a "pre-existing spinal condition" and called it a "scary scene" as he was stabilized before he was carted off the field.
According to Nick Griffith of Fox 31 Denver, the Colts said the injury was to Williams' head, clarifying "he did have activity in his limbs and was strapped on stretcher for precautionary purposes."
The Colts later added that Williams was "awake and alert" with no pain in his neck and movement in his limbs.
Sports Illustrated shared a look at Williams leaving the contest:
ESPN.com's Mike Wells later reported Williams was diagnosed with a concussion and released from the hospital.
"It was a pretty scary thing...but he's back here," head coach Chuck Pagano said, according to Wells. "He's doing well."
The Oregon product hasn't been a featured part of Indianapolis' passing attack this season and has just 13 catches for 121 yards and zero touchdowns. The yardage total is a career high, though, as he managed just 36 in 16 games last season for the Seattle Seahawks.
Williams' injury is another worrisome scene in a prime-time NFL game this season and happens shortly after Pittsburgh Steelers linebacker Ryan Shazier was carted off and hospitalized during a Monday night game against the Cincinnati Bengals in Week 13.
The 3-11 Colts are no longer in playoff contention and are playing out the string of the season.
They will likely rely on Jack Doyle at the tight end spot moving forward for the remainder of Thursday's contest and the last two games of the year.