Officials used containers of water to try and put out the flames
A female suicide bomber has blown up herself in northern Nigeria's Gombe city, minutes after President Goodluck Jonathan left a campaign rally there.
At least one person was killed and 18 others were wounded in the blast, police and hospital sources said.
Mr Jonathan is standing for re-election on 14 February against former military ruler Muhammadu Buhari.
Militant Islamist group Boko Haram has stepped up its attacks in the run-up to the contest.
It has not commented on the blast.
Explosions have also ripped through court buildings in three towns in oil-rich southern Nigeria in what police described as co-ordinated attacks.
Dynamite was suspected to have been used in the attacks in Port Harcourt city and the towns of Isiokpo and Degema in oil-rich Rivers State, regional police spokesman Ahmad Muhammed said.
There were no casualties, but the court building in Degema was "razed down and documents burnt", he is quoted by Nigeria's privately owned Daily Trust newspaper as saying.
Boko Haram is not known to be active in the oil-producing region, where militants demanding a greater share of Nigeria's oil wealth have carried out attacks in the past.
'Angry youth'
In the blast in Gombe, the bomber blew herself up near a car, Gombe state police spokesman Fwaje Atajiri told the BBC.
He said a female passerby had been killed, contradicting earlier reports that three people had been killed in the blast.
President Jonathan addressed his supporters shortly before the blast
Explosions also ripped through the city on Sunday
Residents have set up checkpoints to defend Gombe
Mohammed Bolari, who was at the rally in Gombe, said the explosion occurred some three minutes after Mr Jonathan's departure, AFP news agency reports.
"The president had just passed the parking lot and we were trailing behind his convoy when the explosion happened," he was quoted as saying.
Mr Jonathan addressed a rally in the north-eastern city a day after it was hit by two blasts that killed at least five people.
A local journalist told AFP the latest blast had led to unrest in Gombe, with angry youths attacking supporters of Mr Jonathan's People's Democratic Party (PDP).
"They were shouting and denouncing the president's visit which they blamed for the attack," he added.
A report in the Nigerian paper The Vanguard says the president and Mr Buhari have cancelled scheduled election rallies in Damaturu in Yobe state and Maiduguri in Borno state respectively.
Analysis by Will Ross, BBC News, Nigeria
It may not have been as large as other bombings in Nigeria but the timing of the latest attack will have shocked the security forces. The violence is escalating in the run-up to elections due in less than two weeks.
The attacks are blamed on Boko Haram which is against democracy and says it wants to set up a caliphate.
As well as the bombings the military is facing a huge challenge as the Boko Haram fighters try to capture more territory in the north-east.
On Sunday, the military and local vigilantes prevented the jihadists from penetrating Maiduguri city in Borno state for the second time in a week.
Military aircraft from Chad have meanwhile continued their attacks on Boko Haram positions in north-east Nigeria for a third day.
Eyewitnesses said Chadian jets and helicopters hit targets in the town of Gamboru, just across the border from Cameroon.
Chad sent forces into northern Cameroon in January, driving Boko Haram out of the area but stopping short of advancing on the militants' strongholds deeper inside Nigeria.
Chadian forces are reported to have been massing in the Cameroonian border town of Fotokol since Sunday.
The election is expected to be the most tightly contested since military rule ended in 1999 but there are growing fears that voters in areas controlled by Boko Haram will not be able to vote.
Last week, the African Union (AU) backed plans for the deployment of a 7,500-strong regional force to fight Boko Haram.
Mr Jonathan declared a state of emergency in Nigeria's north-eastern states of Borno, Yobe and Adamawa in May 2013, but it has not stopped the Boko Haram offensive.
BBC AFRICA