Air officials say the airliner was carrying 104 people when it crashed about three kilometres from the airport. Six people survived the crash and were hospitalised.
State radio said the plane crashed during a storm, and witnesses said there was a rainstorm at around the time the aircraft took off.
Debris from the shattered plane, body parts and personal belongings of passengers were strewn over an area the size of a soccer field where the plane went down.
Rescue efforts ended just after 5pm local time (0400 AEDT Monday) as emergency workers removed the last of the bodies recovered to the morgue.
At the airport in Abuja, security officials are keeping away a crush of people seeking information about friends or family aboard the plane.
President Olusegun Obasanjo ordered an immediate investigation into the cause of the crash.
His spokeswoman Remi Oyo said in a statement that the President was "deeply and profoundly shocked and saddened ... he condoles all Nigerians, especially family, friends and associates of those who may have been on board".
The 23-year-old aircraft, a Boeing 737-2B7 owned by Aviation Development Co, a private Nigerian airline, was manufactured in 1983. ADC last suffered a crash in November 1996, when one of its jets plunged into a lagoon outside Nigeria's main city, Lagos, killing all 143 aboard.
Nigeria's air industry is notoriously unsafe. Last year, two planes flying domestic routes crashed within seven weeks of each other, killing 224 people.
Spiritual leader killed
Confirmed among the dead was the man regarded as the spiritual leader of Nigeria’s 70 million Muslims, the sultan of Sokoto, Muhammadu Maccido.
Sulran Maccido headed the National Supreme Council for Islamic Affairs in Nigeria.
Mustapha Shehu, spokesman for the Sokoto state government, had said the sultan's son, Muhammed Maccido, a senator, was also aboard, along with Abdulrahman Shehu Shagari, son of former Nigerian President Shehu Shagari. Their fates were not immediately clear.