Payne, Washington's first-round pick (No. 13 overall) in the 2018 NFL Draft, was hurt during Friday's practice when a teammate stepped on his ankle.
Redskins coach Jay Gruden said Payne, who was the first first-round pick in this year's draft to agree to contract terms, is expected to be in a walking boot for one week.
"He's in great shape so it's not a big deal," Gruden told reporters Saturday. "He's already very smart and knows the defense. He's in good shape."
Payne, who played for national champion Alabama last season, is expected to start at nose tackle for Washington.
The 6-foot-2, 308-pound Payne used the bigger stage of the College Football Playoff to make himself more of household name when he intercepted a pass and caught a touchdown pass in the Crimson Tide's semifinal win over Clemson.
Payne was named the defensive MVP of the Sugar Bowl and the national title game.