A scan on Oram's injured left knee in Auckland yesterday revealed a partial tear of the patella tendon, which gives him no chance of returning at any stage of the five-match series, which the host leads 1-0.
In a statement, team manager Dave Currie said Oram could be sidelined for up to a month.
"It is expected that Jacob will recover in three to four weeks. However, he will be out for the balance of the Australian series," he said.
Central Districts paceman Michael Mason had been summoned to Auckland to bolster the New Zealand bowling stocks, Currie said . Otago all-rounder Ian Butler was not considered because of injury.
The injury gives Oram only a slight chance of playing in the back end of the lucrative Indian Premier League (IPL), starting on March 12, where he has a $US675,000 ($NZ913,795) contract with the Chennai Super Kings.
Oram sustained the injury while fielding in New Zealand's thrilling two-wicket win in Napier on Wednesday when his spikes appeared to catch in the turf and he fell to the ground.
He had delivered seven tidy overs and taken one for 29 as New Zealand out-bowled and out-fielded Australia to restrict it to 275 for eight on a dream batting surface at McLean Park.
The team also did it without Vettori, who withdrew an hour before the match after a chronic neck injury flared up at training the previous day.
Vettori said yesterday his neck was still troubling him and he would test it at training today.
"He's not 100% certain [to play]," Currie said. "The neck was a bit stiff. We're certainly hopeful and he's hopeful, but again we'll get through today and get more treatment and see how he wakes up in the morning."
Meanwhile, Black Caps gloveman Brendon McCullum vowed to keep the pressure on Ricky Ponting's tourists.
"We've got to continue to be aggressive in all facets. They came extremely hard at us at the start of our bowling and the way we responded was brilliant," McCullum said.
That aggression boiled over late in New Zealand's chase when matchwinner Scott Styris (49 not out off 34 balls) and Australian paceman Mitchell Johnson clashed heatedly.
Match referee Ranjan Madugalle later fined Styris 15% of his match fee and Johnson 60% of his.
