Colts head coach Chuck Pagano confirmed that Williams was released from the hospital and was back with the team's medical staff.
"It was a pretty scary thing ... but he's back here," Pagano said after the 25-13 loss. "He's doing well."
Williams suffered the injury in the second quarter and had to be taken off the field at Lucas Oil Stadium on a stretcher.
He was diagnosed with a head injury, but doctors did not preliminarily believe he had suffered an injury to his neck or spine.
Williams, the Colts' primary backup tight end, suffered the injury while blocking Broncos linebacker Deiontrez Mount on a punt early in the quarter. The two players collided, and Mount appeared to try to soften Williams' landing.
Williams remained on the ground the entire time that the medical staff tended to him. Many of the players from both teams took a knee while Williams was strapped onto a stretcher and gingerly loaded onto a cart. The entire Colts team came on the field and went to Williams before he was taken off the field.
Colts tight end Jack Doyle said he was "upset" when he saw his teammate down.
"Worried about him. Worried about his family that's watching on TV," Doyle said. "You think about all those things because Brandon is such a great person, great teammate and great friend. It's just hard to see, so I just hope he'll be all right."
Williams, who has nine catches for 121 yards this season, had his college career at Oregon come to an end a year early because of a spinal condition.
In the summer of 2011, Williams was told he had spinal stenosis, a narrowing of the spinal column. Then-Oregon coach Chip Kelly told Williams that doctors would not give him approval to play because of concern for further injury.
In 2013, an MRI showed the condition had improved, and doctors told him there was nothing to prevent him from playing in the NFL.
"It's a scary thing for all of us, and I'm sure it's scary for his family as well,'' kicker Adam Vinatieri said of Williams. "You hate to see anybody go off like that, teammate or the other team, obviously. I'm hoping that's it's more of a precautionary thing, and I'm hoping that he's going to be OK.''