Gillespie has not featured in pre-tour training camps because of extensive bone bruising and ligament damage in his ankle. It had been hoped the 32-year-old would recover in time for the first Test at Sabina Park on July 27, but instead he will stay at home.
"Mark unfortunately has had to withdraw from the upcoming Test series against the West Indies having not responded to treatment in time to be fully fit," national selection manager Kim Littlejohn said. "As a precautionary measure Mark feels that it would be the right decision to stay in Wellington to continue working on his rehabilitation."
It is another blow for New Zealand in a tour that has already started ominously with a pair of crushing defeats in Twenty20 matches in Florida.
Gillespie returned to the Test fold after a three-and-a-half-year absence in magnificent style back in March, taking five for 59 and six for 113 in consecutive matches against South Africa.
He was then controversially overlooked for a national contract, with injury cited as a contributing factor, and his international future is now again up in the air.
A decision on who will replace Gillespie is yet to be made.
Captain Ross Taylor is also a major doubt for the Test series after a grade two displacement of the left AC joint in his shoulder during the first Twenty20 loss. He is almost certain to be ruled out for the whole of the five-match ODI series.
"We'll have a better assessment over the next week or so and I'll have a better idea of where I'm at. If I'm looking positive I'll stay on. If not I'll come home," Taylor said.
As a result, Kane Williamson looks set to become New Zealand's youngest ever 50-over skipper at 21 years and 332 days in the opening clash in Kingston.