Bravo has returned home to Trinidad "for personal reasons", a team spokesman said.
The left-hander, whose career-best 218 was pivotal in saving the first Test for the West Indies, scored 14 when the West Indies won the first ODI in Auckland on Boxing Day by two wickets.
It was their first taste of success in New Zealand after losing the three-Test series 2-0.
The second of five ODIs is in Napier tomorrow.
Bravo will not be replaced in the West Indies squad for the remaining four ODIs with star batsman Chris Gayle expected to join the squad in time for the two Twenty20 matches.
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