"The investigation was launched over illegal crossing of the state border and violation of international flight regulations," prosecutors in the Baltic EU state said in a press release.
Border guards will conduct the probe and look into the July 4 flight, orchestrated by a Swedish advertising agency.
The plane dropped hundreds of teddy bears attached to little parachutes carrying signs calling for freedom of speech and human rights in Belarus, a move that infuriated the government in Minsk.
Last week, Belarus' authoritarian President Alexander Lukashenko demanded that Vilnius investigate the incident. Minsk also announced it was expelling all Swedish diplomats and closing its embassy in Stockholm.
Lithuania, which joined NATO and the EU in 2004, summoned the Belarus ambassador Tuesday, warning the move could further worsen relations with the European Union.
Meanwhile, the team at Studio Total, the PR firm behind the teddy bear drop, has so far not had a response from President Lukashenko after inviting him to their house in County Skåne, southern Sweden.
The agency's offer followed a summons from the KGB which demanded the team come to Minsk for interrogation.