With regular white-ball captain Mitchell Santner busy in the Indian Premier League, Bracewell skippered New Zealand to a 4-1 victory in a T20 series against Pakistan.
Latham was due to lead New Zealand in the three-match ODI series beginning in Napier on Saturday, but he fractured his hand while batting in the nets and will require at least four weeks to recover, the New Zealand Cricket (NZC) said in a statement on Thursday.
Opener Will Young, meanwhile, will miss the last two ODIs to be with his wife as they await the birth of their first child.
"It's obviously disappointing to lose Tom as captain on the eve of the series and we wish him a speedy recovery," New Zealand head coach Gary Stead said.
"The side is in safe hands with Michael, who's done a great job through the T20I series."
Henry Nicholls will return from a calf strain to replace Latham, while Mitch Hay will keep wickets. Canterbury batsman Rhys Mariu earned his maiden call-up as a batting cover.
"We've had to be flexible this tour with numerous players unavailable for different reasons," Stead said.
"What it does do is offer opportunities to others players and it's nice to introduce Rhys into the environment for the first time, as well as welcome back Henry."Â
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