Rice was placed on the reserve physically unable to perform list Tuesday, the NFL's deadline for reducing rosters to 75 players. Players on reserve don't count toward the active total.
Rice had hip surgery last week and is expected to need at least two months of recovery, so the move was not a surprise. After Minnesota's sixth game, at Green Bay on Oct. 24, the team will have three more weeks to decide whether to activate Rice or end his season by putting him on injured reserve.
The Vikings also waived wide receiver Marko Mitchell and offensive tackle Bill Noethlich and placed linebacker J Leman on injured reserve, after he cleared waivers, to get to the 75-man limit. Noethlich played at Southwest Minnesota State.
The big cutdown comes Saturday, when rosters must trimmed to 53 players. And Rice's injury has further complicated some difficult decisions for the weekend.
After he had the procedure in Vail, Colo., the Vikings signed one wide receiver in Javon Walker and traded for another in Greg Camarillo. But the extra depth at that position cost them at another, with cornerback Benny Sapp being sent to Miami in the deal.
Antoine Winfield is set as one starter, with Lito Sheppard and Asher Allen in competition at the other spot. Rookie Chris Cook, however, was poised to beat both of them out with a strong showing during training camp.
Cook hurt his right knee in Saturday's preseason game against Seattle and was absent from practice Monday and Tuesday. His status was not disclosed by the team.
Incumbent starter Cedric Griffin is not expected to be cleared for the Sept. 9 opener at New Orleans, though he is making progress and has looked strong in drills on his own after practice is over. The Vikings' dilemma for Saturday's roster roulette is whether to free up a roster spot by putting Griffin on the PUP list or bank on him being back in a few more weeks but be short while he gets back to full strength.
Rice, meanwhile, said on his Twitter account Tuesday that he had a "great pool workout" with fellow hip-surgery patient Jonny Flynn, the point guard for the Minnesota Timberwolves. Flynn had his procedure done six weeks ago and is expected to need another two or three months to recover.
Sullivan's availability for New Orleans is increasingly in doubt. Offensive coordinator Darrell Bevell said Sullivan will be re-evaluated after Thursday's preseason game against Denver.
"He'll be fine conditioning-wise, because they're still working on him with that, whether it's in the pool or those other things they can do with him," Bevell said. "We'll just have to see if it can hold up."