The vessel was completely destroyed in the encounter off the northern coast near Talaimannar at about 5:00 p.m. (1100 GMT), he said.
"We spotted a 5.0 gun fixed on to the trawler and we engaged it with gun fire," said the spokesman, Commander D.K.P Dassanayake.
He said divers recovered 120 mortar bombs and 85 rounds of 12.7-millimetre ammunition after the attack.
There was no immediate reaction from the Liberation Tigers of Tamil Eelam (LTTE), whose fight for a Tamil homeland in Sri Lanka's north and east has claimed more than 60,000 lives since 1972.
The navy said Tuesday's attack was the eighth on a boat carrying arms for the rebels this year.
Weekend peace talks between government and rebel representatives in Geneva failed to find agreement on humanitarian issues or a date for further negotiations, dealing another setback to the island.

Copyright AFP (Agence France-Presse), 2006