The flight was operated by SWIFT airline on behalf of DHL and had taken off from Leipzig, Germany before the plane crashed around 0330 GMT, a spokesperson for the governmental National Crisis Management Center said.
All of the people in the house survived, he added.
The spokesperson said there was nothing to suggest an explosion preceded the crash.
"At the moment we don't have any data that there was an explosion", he said.
An airport spokesperson said the plane was a Boeing 737-400 BA.N.
Police told a press conference 12 people had been evacuated from the house hit by the plane.
Rescue services said the plane hit the ground and slid at least 100 metres (110 yards) before crashing into the building.
The head of national crisis management centre said the cause of the crash was being investigated.
Firefighters were seen at 0530 GMT pouring water onto a smoking building some 1.3 km (0.8 mile) north of the airport runway. A large police and ambulance presence was seen nearby and several nearby major streets were cordoned off.
The flight had departed from Leipzig at 0208 GMT, Flightradar24 said on the X social media platform.
Germany is investigating several fires caused by incendiary devices hidden inside parcels at a warehouse in Leipzig earlier this year, the country's prosecutor general said in October.
British counter-terrorism police said shortly afterwards that they were investigating a warehouse fire in July, caused by a package catching alight, and liaising with other European law enforcement agencies to see if there was a connection with similar incidents elsewhere.
