It was not immediately clear if the mosque was used by Sunni or Shia worshippers.
"Security authorities are investigating to identify the assailants and the motives of this criminal act," Saba quoted Taha Hajar, Amran's governor as saying.
Eight victims in critical condition were taken to the capital Sanaa, while 22 were admitted to local hospitals for treatment for burns, the agency said.
Several people suffered from smoke inhalation.
Saba said the attack was the third in Amran.
In 2001, a man opened fire at worshippers, killing three, and in 2003 a bomb exploded in a mosque killing one man and wounding 50, Saba said.
Government officials say at least 250 fighters and about 120 soldiers have been killed since January in a campaign against followers of Shia Muslim rebel leader Abdul-Malik al-Houthi.
Al-Houthi's supporters are not linked to al-Qaeda.