"It is really disappointing for Billy and we know how much he was looking forward to joining the squad," Lions head coach Warren Gatland said.
"He has been carrying an injury and feels he wouldn't be able to contribute fully to the tour and needs further medical treatment.
"We really appreciate his honesty in making this decision and wish him luck with his recovery.
"We have called up James to the squad, we wish him all the best next weekend and look forward to welcoming him into camp before we depart."
The Lions start their 10-match tour against the New Zealand Provincial Barbarians in Whangarei on June 3 and play the All Blacks in the first of three tests on June 24.
Vunipola's older brother and Saracens team mate Mako is in the squad but the loss is regarded as a huge blow to the tourists.
Billy, who has 34 England caps, returned to international rugby in March after missing four months with a knee injury.
Described as a certainty for the test side, he decided after playing in Saracens' Premiership semi-final defeat by Exeter on Saturday that he was not fit enough for the demanding five-week tour.
Scrum-half Ben Youngs had already withdrawn from the squad after his sister-in-law was diagnosed with a terminal illness.