Vunipola missed the autumn Test matches with a calf injury, but returned to the global arena against Ireland, producing an astonishing individual performance in the 32-20 win.
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.
"It is obviously very disappointing to lose Mako at this stage", England head coach Eddie Jones said.
The 28-year-old will now return to his club side Saracens where he will begin his rehabilitation programme.
He missed the November series because of a calf injury, but his recovery from injury alongside brother and No. 8 Billy Vunipola and centre Manu Tuilagi has transformed England into the championship favourite.
However, there was good news for Wales, with Leigh Halfpenny fit to play in the grand-slam eliminator against England on February 23 after overcoming concussion-related symptoms that have dogged him for three months.