Vunipola will be sidelined for about 10 weeks, the English Rugby Union confirmed on Tuesday.
His absence will be a massive blow to England, who have a decisive match against fellow unbeaten side Wales on February 23 in Cardiff.
Vunipola has been prominent in the impressive victories against Ireland and France.
He was man of the match against Ireland in Dublin, and was having a similar impact against France last Saturday until he limped off in the 44th minute at Twickenham.
