No one was injured, crisis management centre head Vilmantas Vitkauskas told Lithuanian radio.
Lithuania is member of the European Union and the NATO military alliance.
"Russia's war of aggression against Ukraine is spilling over onto the eastern flank of NATO and EU," President Gitanas Nauseda had written earlier on X.
He also wrote that a suspected drone had exploded over the north of the country and posed a danger to the civilian population.
Authorities had alerted residents in several regions in the north of the country to a possible threat from the air.
Residents of some Latvian regions bordering Lithuania were also warned.
NATO fighter jets were scrambled to identify the object.
Because of weather conditions, however, no visual contact was possible, Kaunas said.
The minister also said he had proposed a joint investigation of the incident to Poland.
A NATO representative confirmed that two Italian Eurofighter jets were deployed in response to a drone over Lithuanian airspace.
The aircraft were operating under NATO command.
An investigation is under way and NATO is in close contact with Lithuanian authorities, the spokesman said.
According to Vitkauskas, some debris and parts of the object have already been found.
However, it is still unclear whether the drone contained explosives.
In the context of the Ukraine war, there have already been several drone incidents in Lithuania and the other two Baltic countries Estonia and Latvia.
Repeatedly, misdirected Ukrainian drones intended to be used to attack targets in northwestern Russia have entered Baltic airspace and crashed.
Drones of Russian make from Belarus have also entered Lithuania in the past.
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