The incident happened on Žirnių Street at around 5.28 a.m.
All the twelve people registered as residents in the house were evacuated. The fire was localised at around 7.33 a.m.
"We have one casualty. Two crew members were found alive and we are still looking for another one," Head of the Fire and Rescue Department Renatas Požėla told ELTA.
The aircraft was reportedly flying from Leipzig, Germany. Swiftair was operator of the Boeing 757 flight.
Deimantė Matusevičienė, sales manager of DHL Lietuva, UAB, told ELTA she would not comment on the incident.
The police have opened a pre-trial investigation into the plane crash, Ramūnas Matonis, spokesman for the Police Department, told ELTA.
Traffic is currently restricted at the intersection of Liepkalnio and Žirnių Streets.
Planes at Vilnius Airport were given clearance to take off at around 7.40 a.m., after some delay.
LRT public radio earlier reported that the aircraft was small, with two pilots and two crew members possibly aboard.
"A pilot has recovered his consciousness, he has been freed up from the plane and taken to medics," Giedrius Vaičiulis, spokesman for the Fire and Rescue Department, told LRT radio.