The market was crowded with people doing last-minute shopping on the eve of the Eid festival marking the end of the Muslim Holy month of Ramadan.
One witness told the BBC many of the bodies he had seen were of children.
The Islamist militant group Boko Haram has stepped up attacks since President Muhammudu Buhari took office in May.
It has not yet commented on the latest attack.
A trader in the market, Ali Nasiru, told an international news agency that he saw “people lying lifeless on the ground” and traders and shoppers helped in rescue efforts.
The cause of the blasts was not yet known a shopper in the market told the BBC Hausa service, but reports say it was caused by a bomb planted inside a plastic bag.
The attack comes two days after new military chiefs were appointed by President Buhari, who has promised to stem the violence that has plagued the north-east of the country for the last six years.
Boko Haram has targeted markets and bus stations in Gombe city in the past.
Last year, the group took control of a large area of north-eastern Nigeria and declared a caliphate (a state governed in accordance with Islamic law).
Nigeria’s military, backed by troops from neighbouring countries, has recaptured most of the territory, but in recent weeks there has been an upsurge in suicide attacks.
According to Amnesty International, at least 17,000 people, mostly civilians, have been killed since Boko Haram launched its uprising in 2009.
The group is still holding many women, girls and children captive, including 219 schoolgirls it kidnapped from a school in Chibok in April last year.