Bradshaw, who hasn't practiced all week, will miss Sunday's game against the winless Jacksonville Jaguars because of a neck injury he suffered during the second quarter of last weekend's 27-7 win at San Francisco.
His injury clears the way for recently acquired Trent Richardson to assume a primary role in the offense.
"He came in after the last ballgame, had some discomfort in his neck," coach Chuck Pagano said of Bradshaw. "The doctors and trainers are working feverishly to get that thing calmed down."
Bradshaw has a team-high 186 yards on 41 carries for the Colts (2-1).
Richardson, acquired from Cleveland on Sept. 18, becomes the focal point of the backfield. He had 13 carries for 35 yards against the 49ers. Donald Brown will be the backup Sunday.
"It's still going to be a lot of help with Andrew [Luck] and Donald," Richardson said. "Donald is going to help me out a lot. We've all been on the same page. I've been learning the game plan every day."
Defensive lineman Ricky Jean Francois (groin) and safety LaRon Landry (ankle) also will miss the game with injuries. Offensive lineman Donald Thomas (quad), running back Vick Ballard (knee) and tight end Dwayne Allen (hip) are out for the season.