The three other people onboard were injured, and at least one of them was in critical condition.
Flames and smoke engulfed the wrecked plane as fire crews worked to extinguish the blaze.
Lithuanian officials said there was no indication of sabotage so far although Germany is investigating several fires caused by incendiary devices hidden inside parcels at a warehouse in Leipzig for delivery by DHL earlier this year.
German authorities were investigating Monday's crash as well.
European countries have repeatedly expressed concerns about the vulnerability of civilian infrastructure - misgivings which also reared their head after the unexplained severing of two fibre-optic cables in the Baltic Sea last week.
"The fact that we, together with our Lithuanian and Spanish partners, must now seriously ask ourselves whether this was an accident or, after last week, another hybrid incident shows what volatile times we are currently living in, even in the centre of Europe," German Foreign Minister Annalena Baerbock said.
"The German authorities are working very closely with the Lithuanian authorities to get to the bottom of this," she added.
The Boeing 737-400 jet, which went down on Monday morning, was operated by airline Swiftair on behalf of DHL, a German logistics group, and had left Leipzig, Germany, according to Flightradar24.
Lithuanian counter-intelligence chief Darius Jauniskis told reporters: "We cannot reject the possibility of terrorism ... but at the moment we can't make attributions or point fingers because we don't have such information."
In a statement, DHL said the plane "made a forced landing" about 1km from VNO airport and that the cause of the crash was still unknown.
Lithuanian officials meanwhile said there had been no signs of anything unusual from the pilots during radio contact with the aircraft.
"In the recording of the conversation between the pilots and the tower, the pilots until the very last second did not tell the tower of any extraordinary event," Marius Baranauskas, head of the Lithuanian National Aviation Authority, said.
"We need to examine the black boxes to know what was happening in the aircraft."
Vilnius resident Kotryna Ciupailaite said the aircraft flew low over her car as she was driving to work.
"The right wing of the plane turned down before it crashed, as if it was trying to turn. There was something shiny coming out of the right side of the plane, like sparks or a flame, before it hit the ground," Ciupailaite said.
She shared a video with Reuters shot through her vehicle's windshield, which she said was filmed shortly after the crash, showing a big fire beyond a range of trees.
Swiftair said the plane went down in a residential area near Vilnius airport and that it had set up a call centre to assist the relatives of those affected.
Security camera footage showed an aircraft descending behind a warehouse after which the night sky was lit up in bright red and orange, followed by plumes of thick dark smoke.
Rescue services said the plane hit the ground, split into pieces and slid more than 100 metres.
"Only these investigations will answer questions on the real reasons of the incident. Speculations and guesses will really not help to determine the truth," Lithuanian Prime Minister Ingrida Simonyte said in a statement.
A Lithuanian police spokesperson said one person onboard, a Spanish citizen, was killed, and three others - Spanish, German and Lithuanian citizens - were injured.
DHL has launched its own investigation into the crash, a spokeswoman for the company's Lithuanian arm said.
"The aircraft (carried) regular parcels. We do not have any information that any of them were suspicious," she said.
The aircraft was 31 years old, according to a Flightradar24 database.
