Oram, who was sidelined for most of 2005 with a major back problem, flew home at the weekend after experiencing stiffness while bowling in the first Test victory against the hosts.
"It is reassuring to know that it is only a soft tissue injury," he said in a statement.
"I have had some major lower-back problems over my career and while you are always hopeful that the latest problem is not a pointer to something more serious, you can never be certain."
Oram will head to the gym on Wednesday to begin his rehabilitation but it is not yet clear when he will be able to play again.
New Zealand will be hoping he can make a speedy return with Tests against Australia and the West Indies coming up before the end of the year.
"I will be reassessed in a week's time by the medical staff and we should be able to get a better indicator then of when I am likely to get back to the bowling crease," Oram said.