Jamieson experienced stiffness in his left hamstring after travelling back from Bangladesh where the Black Caps fought back in the second test on a difficult Mirpur wicket to level a two-match series at 1-1 last week.
The test squad returned home on Tuesday but Jamieson joined the ODI squad in Dunedin two days later ahead of Sunday's opener and coach Gary Stead said calling up Sears - who is yet to play in ODIs - was a precautionary move.
"We're taking a cautious approach with Kyle," Stead said. "We don't want to rush or push him back, particularly at the very start of our home summer.
"He could play if absolutely necessary but we don't want to take any unnecessary risks, hence calling in Ben for this first match. Ben's familiar to the team environment and it's been good to see him back at full fitness for the Firebirds."
Tom Latham will captain New Zealand with regular skipper Kane Williamson rested alongside Tim Southee, Daryl Mitchell, Mitchell Santner, Glenn Phillips and Devon Conway.
The teams will also play three Twenty20 internationals before the New Year.
