Oram withdrew from the team for the final one-day international against Pakistan on Saturday after injuring his ankle.
However, an MRI scan, X-ray and a medical assessment have all shown there is no lasting damage and the all-rounder will fly as scheduled as the Black Caps start final preparations for the World Cup.
Oram said: "I developed ankle pain and although it didn't feel serious I wasn't able to bowl without discomfort.
"The medical staff got the necessary assessment down and I was sweating on the results but pleased when the doctor let me know that I was fit to travel with the team to the World Cup.
"I have inflammation around the joint so not a significant tear or break.
"I've worked hard over the last six month to get fully fit so it is extremely disappointing to pick up another niggle. However, I am confident it isn't too serious and am determined to do everything I can to be fully fit for the first match."
Oram is expected to be available for the warm-up match against Ireland on February 12.
New Zealand have two warm-up games, the second being against India on February 16.