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.
DHL confirmed that it owned the plane and said it had made an “emergency landing”.
Authorities said they do not have any data at the moment that suggests there was an explosion before the crash.
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.
Mr Pozela said a nearby house was “slightly damaged” and infrastructure near it caught on fire, but all residents were safely evacuated.
The plane was a Boeing 737-400, an airport spokesperson said.
Reported weather before the crash was a temperature of 0C (32F), with clouds before sunrise and winds around 30 km/h (19mph), the Associated Press reported.
The aircraft was 31 years old, AP added.