The Mandala Airlines Boeing 737 was heading to Jakarta when it crashed one minute after takeoff and burst into flames, said Transport Minister Hatta Radjasa.
The plane was carrying 110 passengers and crew, said the airline's acting president, Maj. Gen. Hasril Hamzah Tanjung.
"Only six people survived," said Alex Widjojo, a Mandala spokesman, contradicting earlier reports that all were killed.
Smoke billowed from the burning debris and dozens of houses and at least 10 cars were in flames or damaged. Hundreds of policemen, paramedics and residents were trying to evacuate victims.
The airport in Medan, the largest city on Sumatra island, is close to the center of town and is surrounded by densely populated residential areas.
Indonesia's last crash involving a jetliner occurred in February 2005, when 26 people were killed when a plane operated by Lion Air, another low-cost carrier, skidded off the runway on Java Island, killing 26 people.
Mandala, which is partially owned by the military, has recently slashed the number of flights it operates to stay in business amid aggressive competition by newer airlines. Many of its planes are more than 10 years old.