Vunipola limped off in the second half of Saturday's 13-10 victory over Ireland and will now miss the final two games against Wales and Italy.
"It's a blow as Billy has had a good Six Nations but he is young and will be back," head coach Stuart Lancaster said.
Vunipola sprained his right ankle at Twickenham and a scan on Monday afternoon revealed the extent of the ligament damage.
It is not known how much more of the season the Saracens back row will miss.
Ben Morgan replaced Vunipola against Ireland and will be promoted to the starting line-up for the visit of Wales on Sunday week.
Either Tom Johnson or Matt Kvesic will take Morgan's place on the bench.
"The encouraging thing is that we have Ben Morgan and other back rows such as Matt Kvesic and Tom Johnson who are all competing hard for places," Lancaster said.
- Sports & Recreation
- Stuart Lancaster