Gayle missed the West Indies' final pool match against the United Arab Emirates and has taken only a limited part in training this week because of a chronic back injury for which he has received pain-killing injections. He performed only a light warmup on Saturday before the West Indies' team was confirmed.
The West Indies also chose Sulieman Benn ahead of Kemar Roach.
Fast bowler Adam Milne returned to the New Zealand lineup, displacing Mitchell McClenaghan, after missing New Zealand's final pool match against Bangladesh with a shoulder injury.
His return restores the team used by New Zealand in its first five pool matches and which it has intended to use throughout the tournament.
If New Zealand wins Saturday it will reach the World Cup semifinals for the seventh time and will face South Africa in Auckland on Tuesday. The West Indies won the first two World Cups but haven't reached the semifinals since 1996.
New Zealand also counts the Wellington Regional Stadium as one of its favorite home grounds, having won 10 of its last 12 one-day internationals at the stadium, known locally as the Cake Tin. It beat England by eight wickets in its only previous match at the stadium in this tournament.
McCullum said New Zealand hasn't altered its preparation since the tournament switched from pool to knockout matches and would continue to pursue the aggressive style that had served it well so far.
"In this many game it has a funny, funny way of biting you if you take your eye off the ball," he said. "We know what works for us."
West Indies win toss, bowl in 2nd T20 vs New Zealand