According to the agency, an explosive device was laid on a highway in the northern part of the province, and the bus exploded after hitting it.
Some of those injured are in serious condition.
Yemen has been engulfed in an armed conflict between government forces led by President-in-exile Abdrabuh Mansour Hadi and the armed political opposition Houthi faction movement for several years.
The Saudi-led coalition has been carrying out airstrikes against the Houthis at Hadi's request since March 2015. The conflict has resulted in a massive humanitarian crisis in the poverty-stricken country.