An Aviation Development Company (ADC) official said 105 people were on board the scheduled flight to the northern city of Sokoto when it crashed into a field about 2km from the runway.
Five survivors were rushed to a hospital in Abuja. Two of them were critically ill, an ambulance driver said.
The Sultan of Sokoto, Mohammadu Maccido, spiritual leader of Nigeria's 70 million Muslims, was among those killed.
"The plane crash ... led to the death of our beloved Sultan ... among about 100 people," Attahiru Bafarawathe, governor of Sokoto state, told reporters.
Bafarawa declared six days of mourning for Maccido, who was also the most senior traditional ruler of northern Nigeria and had been instrumental in ending religious bloodshed in the central state of Plateau in 2004.
Mustapha Shehu, spokesman for the Sokoto state government, said that the sultan's son, Muhammed Maccido, a senator, was also on the aeroplane, along with Abdulrahman Shehu Shagari, son of the former Nigerian President Shehu Shagari, who was in office between 1979 and 1983. It was not immediately clear if they had been killed.
Only the plane's tail, an engine and part of a wing were still recognisable at the crash site, which was littered with smouldering fires, boxes and bags.
State radio said the aircraft crashed during a storm and witnesses said there was a rainstorm at around the time the aircraft took off.
Maccido was the spiritual leader
of Nigeria's 70 million Muslims
ADC last suffered a crash in November 1996, when one of its aeroplanes crashed into a lagoon outside the country's main city, Lagos, killing all 143 people onboard.
President Olusegun Obasanjo ordered an immediate investigation into the cause of the crash, his spokeswoman Remi Oyo said in a statement.
Oyo said Obasanjo 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 crash is the third major air accident in Nigeria in just over one year and came just one month before an audit of the country's aviation industry. After last year's crashes, Obasanjo ordered all airlines and aviation authorities to improve safety standards.