There was no immediate word of casualties from Saturday's incident, the latest in a series of clashes stoking fears of a return to civil war.
More than 700 people have died so far this year, straining a 2002 cease-fire between the military and the Liberation Tigers of Tamil Eelam (LTTE).
Commander DKP Dassanayake, a navy spokesman, said early on Saturday: "The navy fired and destroyed one Tamil Tiger boat approaching Kankesanturai in Jaffna. The boat ignored our warnings to stop, so we fired.
"Generally such boats have two or three people aboard."
In a separate incident, Nordic truce monitors reported heavy artillery fire in the eastern district of Trincomalee. The army had no details.
LTTE had no immediate comment on either incident.
The clash comes just days after a flotilla of about 20 rebel boats attacked two small navy vessels near a northwestern base in an attack that killed five sailors and at least one rebel.
It also follows a string of ambushes, shootings and military clashes which culminated in last week's assassination of one of the country's top generals by a suspected Tamil Tiger who rammed his explosives-laden motorcycle into an army convoy near the capital, Colombo.
Sri Lanka's peace process is deadlocked and on the brink of collapse. Government and rebels are sharply divided over the Tigers' demands for a separate homeland for minority Tamils in the north and east.