The Saracens back-rower was forced off before half time in the 23-12 loss to South Africa which marks England's fifth successive Test defeat to ramp up the pressure on coach Eddie Jones.
The injury came six months after first breaking his arm in Saracens' European Champions Cup tie with Ospreys.
It is the latest injury in a long line for Vunipola dating back to the 2015 World Cup when he injured his knee ligaments against Wales in the pool stages.
Since then he has had knee surgery after suffering further issues, keeping him out of the British & Irish Lions tour of New Zealand in 2017, before breaking his arm for the first time, leading to his absence from the Six Nations.
England have been hit hard by injuries and squad exits in the wake of the South Africa loss with Mako Vunipola leaving the squad to attend the birth of his child, while Ellis Genge has already flown back to London after suffering a knee injury in training.
The 23-12 loss means the Springboks sealed victory in the summer series with Saturday's game at Newlands still to come.