Kulasekara was driving a car which collided with a motorbike on Monday, instantly killing the rider.
Citing initial investigations, Sri Lanka Cricket said the motorcyclist lost control while trying to overtake a bus and was flung into Kulasekara's path.
The 34-year-old seam bowler last played for Sri Lanka in March in the World Twenty20.
In June, he retired from test cricket after 21 matches to concentrate on one-day internationals and T20s.