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.
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.
"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," England coach Eddie Jones said.
Ben Moon replaced Vunipola on Saturday, and Ellis Genge and Alec Hepburn are also options.
Wales No. 8 Taulupe Faletau has also been ruled out of the Six Nations because he needs another operation on his fractured arm.
The 28-year-old sustained the injury while playing in his comeback match with English club Bath.
"We're gutted for Taulupe, but this is the best course of action for him moving forwards as a player," Bath director of rugby Todd Blackadder said.