Davis -- the team's leading receiver with 312 yards on 23 catches -- sustained the injury Sunday in the first quarter of Washington's 27-23 loss to the New York Giants.
The fifth-year pro went down in the end zone after trying to make a cut and had to be carted off the field.
"Achilles ... right now it's a tear," Shanahan told reporters after the game. "He'll be out for the year."
Celebrity Families of 2014 [PHOTOS]