Two residents reported the blasts and said they heard the sound of ambulances. The local official told Reuters the Houthis had fired a missile and an armed drone at the city.
There was no confirmation from the Iran-aligned movement, which has launched an offensive to take the internationally recognised government's last stronghold in the north of the Arabian Peninsula country.
It was not immediately clear if there were any casualties from the explosions.
Earlier this month at least 17 people were killed in an explosion near a petrol station in Marib. The government said it was caused by a Houthi missile, but the group said it had only hit a military camp.
Yemen has been mired in violence since the Houthis ousted the Saudi-backed government from the capital, Sanaa, in late 2014, prompting a military coalition led by Saudi Arabia to intervene months later.
The United Nations, backed by the United States, is pressing for a nationwide ceasefire.