"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 at 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.
Thursday's attacks came two days after 16 schoolgirls were among 26 people killed in a car bomb attack targeting a Shiite militia leader in the central town of Rada.
Yemen has been rocked by worsening instability since the Shiite fighters, who are also known as Huthis, seized control of the capital Sanaa on September 21.
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The Huthis have since expanded their presence in central and western Yemen, including Hodeida, but have met fierce resistance from Sunni tribes and Al-Qaeda militants.
Thursday's attack came as a new Yemeni government won a confidence vote in parliament a month after its formation.
The government of Prime Minister Khaled Bahah was formed as part of a UN-brokered peace deal aimed at restoring stability.
Made up of technocrats, the government was agreed with the Huthis and its formation was meant to pave the way for them to loosen their hold on Sanaa, though there have been no signs of the militia abandoning positions.
President Abdrabuh Mansur Hadi has struggled to assert his authority since the Huthi takeover of the capital.
Instability has dogged Yemen since an Arab Spring-inspired uprising forced Ali Abdullah Saleh from power in 2012, with the Huthis and Al-Qaeda among those seeking to fill the power vacuum.
The turmoil has raised fears that the Arabian Peninsula nation, which neighbours oil-rich Saudi Arabia and lies on the key shipping route from the Suez Canal to the Gulf, may become a failed state.