Vinatieri, who said he started feeling pain in his knee last week, did not practice Thursday or Friday after being a limited participant Wednesday. It will be the first game he has missed due to injury since 2009.
Reich said they have not talked about putting Vinatieri on the season-ending injured reserve list, instead classifying the kicker as being "week to week" with four games left in the regular season.
Vinatieri, 46, dealt with a similar knee problem during training camp.
He has made a career-low 68% of his field goal attempts this season and missed 14 kicks -- eight field goals and six extra points. Two of Vinatieri's misses -- against the Chargers and Steelers -- cost the Colts games.
Chase McLaughlin, who the Colts claimed off waivers Wednesday, will handle the kicking duties. McLaughlin has played in seven games this season, four with the Chargers and three with the San Francisco 49ers. He was 13-for-17 on field goals and made all 15 of his extra point attempts.
The Colts will get some help on offense, as running back Marlon Mack (hand), who has rushed for a team-high 862 yards, and rookie receiver Parris Campbell (hand) are expected to return, barring any setback after missing two and four games, respectively.