Qat is a mild narcotic and mainstay of Yemeni social life whose consumption is banned in parts of the country held by the jihadist Al-Qaeda in the Arabian Peninsula (AQAP).
The official said the bomb was planted at the entrance of the market by unknown individuals who apparently wanted to target loyalist forces.
Marib is east of the capital Sanaa which is in the hands of Shiite Huthi rebels.
The rebels said on their website sabanews.Net that three bombs exploded at the qat market, killing seven people and wounding 15.
The latest violence comes as talks aimed at ending a 13-month devastating war in Yemen are under way in Kuwait between government and rebel delegations.