The right-hander sustained the problem during the recent ODI series against the same opposition. Dimuth Karunaratne has been drafted in to replace the veteran for the match in Galle.
The 24-year-old left-hander, who has made two ODI appearances, will make his Test debut on Saturday if selected.
New Zealand will be looking for revenge in the longer format after being comprehensively defeated in the ODIs.
The second and final Test follows in Colombo from November 25.
