Fleming was hit by a ball on the middle finger during fielding practice, and an x-ray confirmed he had broken off a piece of bone at the base of the finger, New Zealand manager Lindsay Crocker said in a statement on Wednesday.
It was uncertain how long Fleming would be sidelined.
The injury happened during the warm-up practice before the third day of a provincial match between Fleming's Wellington side and Central Districts.
"Stephen was able to bat in the match but it will be 24 hours before we know the extent of the injury," Crocker said.
Fleming batted at number five for Wellington after the x-ray, but was dismissed leg before wicket for seven.
It continued an unhappy run for the captain who missed the first two matches of the recent Chappell-Hadlee series against Australia after having a benign tumour removed from his jaw.
New Zealand host Sri Lanka in four one-day internationals starting at Queenstown on December 31, with coach John Bracewell due to name his team on Friday.