The twin car bombings targeted concentrations of Shiite Houthi militiamen in the city, eyewitnesses told The Anadolu Agency.
They added that the attacks had occurred near the home of Yemeni army general Ali Mohsen al-Ahmar, which had been occupied by the Houthis since they entered Al-Hudaydah.
None of the eyewitnesses, however, could provide an exact death toll.
A pro-Houthi newspaper, meanwhile, reported on its Facebook page that a number of Islamists and two suicide bombers had been on board the booby-trapped vehicles.
The newspaper added that Houthi vigilantes had managed to kill three other suicide bombers before they blew themselves up in the same area.
The Houthis have remained in control of capital Sanaa since late September. Ever since, the group has moved to extend its control to other areas, including Al-Hudaydah on the Red Sea coast.
The Houthis' growing influence in Yemen has pitted the Shiite group against Al-Qaeda – still said to be active in the fractious country – and local Sunni tribes.