New Zealand captain Daniel Vettori is expected to return for the second match of the Chappell-Hadlee series against Australia in Auckland on Saturday.
Vettori was a late withdrawal from the series opener with a neck injury but the problem is not believed to be serious.
Ross Taylor took charge in Vettori's absence as the Black Caps claimed a two-wicket victory in Napier to strike first in the five-match series.
"Vettori's neck had a kink in it on Tuesday but he thought he would be all right," said New Zealand team manager David Currie.
"Even warming up on Wednesday he thought he would be all right but he wasn't and there was no point taking any risk on it.
"He is fully expected to be back next game."
However, the news on Jacob Oram is less positive with the New Zealand all-rounder almost certain to miss the second one-day international due to a knee injury.
Oram sustained the problem while fielding in Napier and had to be helped from the field midway through Australia's innings.
He took no further part in proceedings and could miss the remainder of the series.
"Jacob's knee is painful," said Currie. "There will be further investigation in Auckland and we'll assess after that.
"It's pretty painful at the moment so we'll have to wait and see."
Meanwhile, Scott Styris and Mitchell Johnson have each been fined for their on-field spat during the first one-day international.
New Zealand all-rounder Styris was fined 15 percent of his match fee for a level one offence and Australia left-arm paceman Johnson was docked 60 percent of his match fee at level two.
Both pleaded guilty to breaching the International Cricket Council's code of conduct during an incident came at the end of the 46th over of New Zealand's run chase.
An initial verbal exchange was followed by "deliberate and inappropriate physical contact" on Johnson's part. The players appeared to bump shoulders, and then heads too.
"Sometimes in the heat of competition players cross over the line of what is acceptable behaviour, and that has clearly happened in this case," said match referee Ranjan Madugalle, who did not need to conduct a full disciplinary hearing as both players accepted their guilt.
"I made it clear to them that as role models it's important they conduct themselves not only within the laws of cricket but also in keeping with the spirit of the game."