The clash erupted when southern secessionists attempted to storm the governorate building to hoist a flag of the former South Yemen, which was an independent state until it was united with the north in 1990.
Four policemen, four armed men and seven civilians were wounded, the sources said.
In southeastern Yemen, meanwhile, soldiers clashed with armed tribesmen east of the city of Mukalla, military sources said.
The tribesmen attacked troops stationed near an oil installation in the area of Ghail Bayamin, with the aim of driving forces away to take their place.
Violence has intensified in south Yemen amid tribal anger over the killing of a local chief and his bodyguards at a checkpoint earlier this month.