The unidentified aircraft was detected heading towards the island's northeastern coast near Mullaittivu, the last town under the control of the Liberation Tigers of Tamil Eelam (LTTE), officials said.
"The aircraft was seen over northern waters and heading towards Mullaittivu district late Tuesday," said a military official who declined to be named.
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"Naval vessels in the area had opened fire, but the aircraft had disappeared."
Sri Lanka's air force said it did not believe the plane was a light aircraft of the kind belonging to the LTTE and used in the past for attacks across the island.
"It couldn't have been an LTTE aircraft because what was observed was at a high altitude," said air force spokesman Wing Commander Janaka Nanayakkara.
Tiger rebels carried out their last flying mission in September when they bombed a military base in the north of the island.
Since then, Sri Lanka's army has captured six LTTE jungle airstrips.