The move ends Vinatieri's 24th season in the NFL -- and potentially his career.
Vinatieri, 46, was inactive for Sunday's loss to the Tampa Bay Buccaneers and has struggled throughout the season, making just 17 of 25 field goal attempts and 22 of 28 extra points.
"I haven't had a long heart-to-heart with him yet, but it's my understanding that in his mind, Adam's not done," Colts coach Frank Reich said. "That doesn't surprise me. That guy inspires me."
Reich said the Colts "knew he had the issue in the preseason, missed a couple of weeks with the knee, but once we got going it was never really on the injury report."
Reich added: "Adam, he's a tough guy. Whatever pain he was dealing with, was him dealing with it. Like every other player dealing with pain, it's not uncommon. He wasn't being irresponsible to the team. Everybody has aches and pains you play through. He was performing out in practice. There was nothing that was limiting him."
Asked if he though the injury played a factor in Vinatieri's 14 missed kicks this season, Reich said: "At some level it had to affect him."
The Colts added insurance at the kicking position last Wednesday when they claimed Chase McLaughlin, who made 2 of 3 field goals and all three of his PATs on Sunday.
Vinatieri routinely had said that his knee wasn't a problem, but he went from being one of the most reliable kickers in league history to one of the weakest links on the Indianapolis roster this season.
The Colts, despite working out 11 kickers at two different times this season, stuck with Vinatieri even though he made a career-low 68% of his field goal attempts this season. Two of Vinatieri's misses -- at the Chargers and at Pittsburgh -- cost the Colts games.
If this season is Vinatieri's last, he'll finish as the NFL's leading career scorer with 2,671 points and with 29 game-winning kicks. Three of Vinatieri's most memorable winning kicks occurred when he was with the New England Patriots from 1996 to 2005. He made a game winner in blizzard-like conditions against Oakland in the 2001 playoffs and winning kicks in Super Bowls XXXVI and XXXVIII.
Also Monday, the Colts placed receiver Parris Campbell on injured reserve. Campbell suffered a broken foot in Sunday's loss to the Buccaneers.
ESPN's Mike Wells contributed to this report.