The blast happened at about 7:40pm on Thursday at the Jimeta Main Market in the Adamawa state capital, just as traders were finishing business for the evening.
"So far, we have 31 dead victims and 38 people in hospital receiving treatment" as a result of the blast, said Sa'ad Bello, Yola's National Emergency Management Agency coordinator.
"Some whose injuries were not severe were discharged," he told the AFP news agency.
In recent years, Yola has come to be seen as a relative safe haven for hundreds of thousands of people forced to flee their homes because of ongoing violence in the country.
There was no immediate claim of responsibility but fingers will likely be pointed at Boko Haram, which has carried out several attacks in the north of the state in recent weeks.
More than 60 people have been killed in attacks since the weekend in Maiduguri, the northeastern city that is the birthplace of the armed group.
The violence poses a great challenge to the country's new president, Muhammadu Buhari, who announced on Friday that he is moving the military's headquarters from the capital Abuja to Maiduguri to better tackle Boko Haram.