Colts coach Tony Dungy declined Thursday to elaborate on Vinatieri's injury, saying he expected a team doctor to give an update about the kicker's recovery Friday.
Team spokesman Craig Kelly said Vinatieri had not suffered any broken bones and that he was recovering from a sprained ligament.
A source with the Colts told ESPN.com's Michael Smith that Vinatieri will not kick in Friday night's preseason game against Cincinnati, but barring further injury, he will kick in the Sept. 10 season opener against the Giants.
The Indianapolis Star had reported earlier Thursday that Vinatieri has a broken bone in his left foot, which he uses to plant before kicking.
"That's what he told us about a week and a half ago," Vinatieri's mother, Judy, told the newspaper. "They sent him to a specialist. They found a small broken bone in his foot."
Arguably the best pressure kicker in NFL history, Vinatieri left his long-time home with the New England Patriots this past offseason and signed a five-year deal with the Colts.
Vinatieri, 33, made 82 percent (263-of-321) of his field goals in 10 seasons with the Patriots. He has replaced Mike Vanderjagt, who converted 87.5 percent (217-of-248) in eight years with the Colts.
But Vanderjagt did not come through when the Colts needed him most, missing a 46-yard attempt with 17 seconds left in a 21-18 loss to the Pittsburgh Steelers in the AFC divisional playoffs in January.
Vinatieri made virtually every clutch kick for the Patriots, helping them become the second team in NFL history to win three Super Bowls in a four-year span (2001-04).
He kicked a 48-yard field goal as time expired to give the Patriots a 20-17 victory over the St. Louis Rams in Super Bowl XXXVI and drilled a 41-yarder with four seconds left in a 32-29 win over Carolina in Super Bowl XXXVIII.
The Patriots would not even have made the Super Bowl in the first year of their title run without Vinatieri, who kicked a game-tying 45-yard field goal in a heavy snowfall with 27 seconds left in regulation and booted a 23-yarder in overtime in a divisional playoff win over Oakland.
Information from SportsTicker and the Associated Press was used in this report.