The blast targeted a market selling qat on Wednesday, the mild narcotic leaf popular in the Arabian Peninsula country, a security official in Marib said.
Forces loyal to Yemen's President Abd Rabbo Mansour Hadi control Marib, which is east of Yemen's rebel-held capital Sanaa.
The province of Marib has seen fierce battles between Hadi loyalists and Houthi rebels and their allies, who continue to control northern parts of the governorate.
A Saudi-led coalition which intervened in Yemen in March 2015 against the rebels has forces based in Marib province to support the government loyalists.
Al-Qaeda and Islamic State group militants have found ground amid the chaos, and launched a wave of bombings across the country - targeting both pro- and anti-government forces and civilians.
More than 6,400 Yemenis have been killed since last March - most of them civilians - and the fighting has driven 2.8 million people from their homes.