Local sources confirmed that four prisoners were injured in this explosion.
Also on Thursday, police fired tear gas to disperse protesters in Dali and several other southern towns.
The demonstrators were protesting the government's ongoing crackdown against southern pro-secession activists.
Police officials said scores of protesters were detained.
Tensions have recently escalated in the south, adding to the challenge Yemen's government already faces from an al-Qaeda movement that has set up operations there and a northern rebellion.
Widespread demonstrations have taken place in Yemen in recent months,with crowds calling for the military to withdraw from southern cities and for the government to halt a sweeping campaign of arrests.
South Yemen was independent from 1967 until it united with the north in 1990.
An attempt to break away again in 1994 sparked a short-lived civil war that ended when the south was overrun by northern troops.