Ukraine said it had apologised for the incident and that the drone fired in its war with Russia had gone astray, most likely because of Russian electronic interference.
There were no reported injuries or damage from the crash in Finland's southeast, the first time the Russia-Ukraine war has spilled onto its soil.
Ukraine has stepped up drone attacks on Russian oil refineries and export routes over recent weeks, some close to Russia's border with Finland, in an attempt to weaken the Russian war economy.
"These are individual Ukrainian drones that have strayed into our territory," Air Force Commander Major General Timo Herranen said on Monday.
"The UAV (Unmanned Aerial Vehicle) that came down north of Kouvola was found, in a preliminary assessment by the authorities, to have an unexploded warhead attached," Finnish police said in a statement.
It was identified as a Ukrainian AN-196 drone, with a wingspan of 6.7 metres, and was destroyed in a controlled detonation.
Debris from a second drone, also thought to be Ukrainian, was found in the municipality of Luumaki, east of the town of Kouvola, and officers were investigating whether it detonated when it crashed, police added.
"We can confirm that under no circumstances were any Ukrainian drones directed towards Finland ... We have already apologised to the Finnish side for this incident," Ukraine's foreign ministry spokesman said.
Finland's President Alexander Stubb and Ukrainian leader Volodymyr Zelenskiy discussed the incident in a phone call on Monday.
"Alex and I see the situation in the same way. We are sharing all necessary information," Zelenskiy wrote on social media.
Some of Ukraine's allies sent it "signals" about the possibility of scaling back its long-range strikes on Russia's oil sector amid a spike in global energy prices, Zelenskiy said on Monday.
Speaking to reporters in a WhatsApp chat, he added that Ukraine was ready to reciprocate if Russia stops attacking the Ukrainian energy system, and that Ukraine is open to an Easter ceasefire.
"Recently, following such a severe global energy crisis, we have indeed received signals from some of our partners about how to reduce our responses in the oil sector and the energy sector of the Russian Federation," Zelenskiy said in a WhatsApp briefing with journalists.
Stubb did not ask Ukraine to reduce its strikes on Russian assets in Finland's vicinity in the call with Zelenskiy, Stubb's office told Reuters.
"This was not discussed between the presidents," it said in an emailed statement.
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