Nearby countries Estonia, Latvia and Lithuania said last week that several Ukrainian drones had crashed on their territory after going astray during attacks on Russian oil export facilities on the Baltic Sea coast.
Ukraine has stepped up drone attacks on Russian oil refineries and export routes over recent weeks in an attempt to weaken Russia's war economy and as peace talks, brokered by Washington, have stalled.
On Sunday morning, several small, slow-moving objects flying at low altitude were detected over a maritime area and in southeastern Finland, the defence ministry said in a statement.
Finland's Prime Minister Petteri Orpo said the stray drones seemed to be linked to Ukraine's attacks on Russian targets in Finland's vicinity.
"Russia has extremely strong electronic jamming capabilities, which could explain why these drones are drifting into Finnish airspace, something that is a very serious issue," Orpo told Finland's public broadcaster Yle.
Finland sent its F/A-18 Hornet fighter jets to identify the flying objects that approached its territorial waters, one of which was identified as a Ukrainian AN196 drone, the Finnish Air Force said.
"The pilot did not open fire in order to avoid collateral damage," it said in a statement, adding the drone fell to the ground north of the town of Kouvola in eastern Finland.
Another drone hit the ground in the same region, it said.
Ukraine has hit all three major oil ports in western Russia this month: Novorossiysk on the Black Sea and Primorsk and Ust-Luga on the Baltic Sea in Finland's vicinity.