The 23-year-old dislocated the patella in his right knee in Saracens' 23-6 Heineken Cup final defeat to Toulon in Cardiff last weekend.
England's second set of tourists fly out to New Zealand on Monday and Vunipola's knee problem further deepens England's injury concerns at loosehead prop, with Joe Marler suffering a hip complaint. England called up Bath's Nathan Catt as late cover for Marler in the initial group of tourists that flew out to New Zealand on Tuesday.
Wasps' three-cap loosehead Matt Mullan will now start England's first Test against the All Blacks in Auckland on June 7 unless Marler makes a rapid recovery.
Meanwhile, Schalk Brits has spent four months pleading with Saracens captain Steve Borthwick not to retire after today's climax to the English domestic season.
The livewire Springboks hooker believes that gritty lock Borthwick is the "yin to my yang", admitting that the former England skipper will be all but irreplaceable at Allianz Park.
Borthwick will wrap up 16 years of top-flight rugby in the Twickenham league battle against Northampton, before joining Japan's coaching ranks full time.