Team manager Charith Senanayake said on Sunday that the extent of Kulasekara's injury was not yet known but confirmed the player will not take any further part in the series.
"We cannot get a scan here in Hambantota. We will get a scan done when we reach Colombo and see the extent of the injury and for how long he will be out," he said.
A replacement for Kulasekara will be named shortly, added Senanayake.
Kulasekara injured himself while attempting to catch Indian batsman Virender Sehwag in the 11th over while fielding at mid-off during the first game, won by India.
The second match takes place on July 24 at Hambantota.