The aircraft departed from DHL’s hub at Leipzig Airport just after 03:00 local time (02:00 GMT) and crashed around an hour and a half later, according to data from flight-tracking website Flightradar24.
Flight operations are continuing at Vilnius airport as authorities respond to the crash, Flightradar24 said on X.
Firefighters were seen tackling smoke coming from a building 1.3 km (0.8 mile) north of the airport runway, Reuters news agency reported.
The cause of the crash is unknown and Lithuanian authorities have started an investigation.
The head of Lithuania’s firefighting and emergency services unit, Renatas Pozela, said the plane was due to land at Vilnius airport and “crashed a few kilometres away”.
One person in the four-member crew died, he added.