Police spokesman Ajith Rohana said the would-be asylum seekers were arrested at the southwestern fisheries harbour of Beruwela. Those arrested include nine women and six children, he said.
Authorities said an initial probe suggested that the group included a former Tamil Tiger rebel.
The police said they believe it was the first attempt by Sri Lankans to travel to New Zealand for asylum.
Australia, a favourite destination for asylum seekers from Sri Lanka, recently sent back to 45 Sri Lankans who tried to enter the country illegally.