Most of the victims are believed to be residents of the village of Dacha-Suu, where the Boeing 747 came down in dense fog near Manas airport.
The plane reportedly crashed as it tried to land at around 7.30am local time (1.30am UK time) in an area of the capital Biskek with a number of summer houses.
Mukhammed Svarov, head of the crisis management centre at the emergencies ministry, said the plane ploughed through the village for several hundred metres, damaging 15 buildings.
"The damage to infrastructure in the village is significant," he said.
He added that the number of dead "could be bigger" than the 37 fatalities confirmed so far.
"The plane crashed into the houses, it killed entire families," a witness told AFP.
"There's nothing left of the houses, people were killed with their whole family, their children. Many people were sleeping."
Airport officials said the jet had been due to make a stopover at Manas on its way from Hong Kong to Istanbul.
Kyrgyzstan's transport ministry said there were five people on board.
It identified the plane as a Turkish Airlines Boeing 747-400, but the company said it belonged to another Turkish firm, ACT Airlines.
"Our condolences to the families of those who have lost their lives in the tragic incident involving an ACT Airlines aircraft in Kyrgyzstan," Turkish Airlines said on its Twitter account.
ACT said in a statement: "Our TC-MCL signed plane, flying on Jan. 16 from Hong Kong to Bishkek, crashed on landing at Bishkek at the end of the runway for an unknown reason."