Griffin, who is having an outstanding rookie season as the Redskins' starting quarterback, was injured late in Sunday's game against Baltimore.
Kirk Cousins, also a rookie, replaced Griffin and led Washington to the tying touchdown -- running in the 2-point conversion himself -- and the Redskins were able to beat the Ravens 31-28 in overtime.
Griffin was examined Sunday night and was found to have a Grade I sprain of the lateral collateral ligament.
"We're going to do what [is] in Robert's best interests, as well as the football team," Shanahan said Monday, adding he wasn't sure if Griffin would be able to practice Wednesday.
He added a decision on whether Griffin could play Sunday when Washington plays Cleveland would be reached later in the week.
The Redskins, who have won their last four games, are tied with Dallas at 7-6 in the NFC East, one game behind the New York Giants.
Griffin has started every game for Washington this season, completing 233-of-351 passes for 2,906 yards, 18 touchdowns and four interceptions. He's also rushed for 748 yards -- second high on the teams.