Vunipola picked up the injury during the 44th minute of Sunday’s 44-8 win over France at Twickenham and watched the rest of the game with ice strapped to his left ankle.
The 28-year-old is expected to be sidelined for 10 weeks, which also rules him out of Saracens’ Champions Cup quarter-final against Glasgow.
Vunipola will return to Sarries to begin his rehabilitation.
England head coach Eddie Jones said: “It is obviously very disappointing to lose Mako at this stage as he is an important player for us but it does provide an opportunity for the team to grow.”
Vunipola was man of the match in England’s opening-round win over defending champions Ireland and his injury is a major blow ahead of the Cardiff showdown with Wales on February 23.
Vunipola’s absence opens the door at loosehead for Ellis Genge and Ben Moon, who were replacements against Ireland and France respectively, as well as Exeter’s Alec Hepburn.
The England squad will assemble in London on Wednesday for a three-day camp ahead of the Wales game.