Oram suffered a hairline fracture to his left index finger attempting a catch in the gully while playing for Central Districts against Northern Districts.
The match was Oram's first outing since injuring his back in the first test against Bangladesh in Chittagong over a month ago. He missed the current series against Australia to recover.
"I've got to a point now where I wasn't disappointed, I just had a laugh," Oram told Radio Sport.
"I just thought, 'who have I annoyed so much to keep throwing this at me'. Hopefully it's character-building."
An x-ray cleared him of any tendon damage but it is uncertain how much impact the injury will have on the 30-year-old.
Oram, who has now suffered at least five broken fingers in his career, said if the swelling went down he was keen to play a role in the final three days of the current match.
The first test against the West Indies starts in Dunedin on December 11.