Aliyu Maikano, an official with the Nigerian Red Cross, said the blast in the Jimeta area of the city was caused by an "explosive device".
The blast "wrought massive destruction on the building" and sparked a fire, he added.
"We've been told by security personnel that there are two more explosives that are yet to detonate," said Maikano.
"All rescue respondents are staying outside from a distance waiting for a signal from the security agents to go in and start rescue operations.
The explosion, which happened at 11:30 am (1030 GMT), was confirmed by two local residents, while the National Emergency Management Agency (NEMA) said it was responding to a "bomb blast".
Yola has been targeted before as part of Boko Haram's Islamist insurgency in northeast Nigeria, which has left at least 17,000 people dead since 2009.
On November 17 last year, at least 34 people were killed and 80 others injured when an improvised explosive device (IED) went off at a lorry park in the Jambutu area of the city.
An IED left at a camp for people displaced by the conflict in Malkohi, just outside Yola, killed seven on September 11.
There was no immediate claim of responsibility for the explosion or an indication of what caused it, but Boko Haram has previously targeted police stations and government buildings.
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