"The two explosions were the result of two car bombs and left dozens dead and wounded," the official told AFP, without providing any precise figures.
The first bomb detonated close to the Hodeida headquarters of the Shiite militia known as Ansarullah which seized the town at the end of September, said the official.
The other bomb went off close to another position of the Shiite militia west of Hodeida University, not far from the site of the first attack.
Yemen has been rocked by instability since the Shiite fighters, who are also known as Huthis, seized control of the capital Sanaa on September 21.
The Huthis have since expanded their presence in central and western Yemen, including Hodeida, but have been met by fierce resistance from Sunni tribes and Al-Qaeda militants.