Oram will definitely miss the remaining two matches of the Chappell-Hadlee Series against Australia and his future after that is clouded after fracturing his left ring finger.
"Jacob will see a specialist in Hamilton on Monday to determine the management of the injury," New Zealand manager Lindsay Crocker said.
"He will remain with the squad to keep on track with his World Cup preparations. At this stage, we are confident he will travel to the World Cup."
Oram fractured the finger when catching Mitchell Johnson late in Australia's innings of 148 in the first match of the series in Wellington on Friday night.
New Zealand surpassed that total without loss in just 27 overs to inflict Australia's first defeat without taking a wicket.
Oram is a central figure in the New Zealand team and with his medium-fast bowling he recorded a respectable 0-22 off 10 overs to help ensure Australia could not muster a defendable total.
Although the big-hitter was not required to bat, in the recent tri-series against Australia and England he averaged 87 at a strike rate of 124.28 runs per 100 balls.
If Oram is cleared to play in the World Cup he may miss New Zealand's opening game against England on March 16.
New Zealand also has group games against minnows Kenya and Canada before the Super Eight stage determines the semifinalists.
Oram is the third casualty of the Chappell-Hadlee series being used by New Zealand to fine tune ahead of the World Cup.
Australian fast bowler Brett Lee has gone home with an ankle injury and batsman Michael Clarke has been ruled out with a hip problem.