Latham will be skipper for the white-ball matches at Auckland’s Eden Park on March 25, Christchurch three days later and Hamilton on March 31.
Kane Williamson (Gujarat Titans), Tim Southee (Kolkata Knight Riders), Devon Conway and Mitchell Santner (both Chennai Super Kings) are not available, New Zealand Cricket said.
The quartet will join their Indian franchises after the second Test against Sri Lanka, which starts in Wellington on Friday.
Williamson steered New Zealand to a thrilling last-ball win over Sri Lanka in the first Test on Monday on a rain-disrupted final day in Christchurch.
With a host of stars absent, Black Caps coach Gary Stead has added South African-born batter Chad Bowes and seamer Ben Lister to the ODI squad.
Lister made his Twenty20 debut in India last month while this is the first time Bowes has been selected for the Black Caps.
New Zealand will host Sri Lanka in three Twenty20 matches following the ODI series.
ODI Squad to face Sri Lanka from: Tom Latham (c), Finn Allen, Tom Blundell, Chad Bowes, Michael Bracewell, Mark Chapman, Lockie Ferguson, Matt Henry, Ben Lister, Daryl Mitchell, Henry Nicholls, Glenn Phillips, Henry Shipley, Ish Sodhi, Blair Tickner, Will Young.