The attack was the first in the current conflict on Aden's al-Maashiq palace, the seat of Yemen's Saudi-backed and internationally recognised government.
The government's prime minister and cabinet members were safe following the attack, Yemeni Information Minister Moammar al-Eryani said.
Witnesses told Reuters they heard loud booms near the palace.
Yemen's cabinet said the attack involved missiles and drones, and officials told Reuters that two guards were killed.
Houthi military spokesman Yahya Saree said the Houthi rebels had bombed what he described as the Saudi military operations headquarters in Aden as part of the group's declared policy of targeting "Saudi reinforcements wherever they were located".
The Houthi-run news agency SABA said the headquarters was run by Saudi officers and that there were weapons depots there.
Reuters could not independently verify the claims.
The renewed fighting between the Iran-aligned Houthi rebels and Saudi-backed government forces resumed in Yemen last month, and aid agencies have warned of rapidly worsening conditions.
Last week, government forces launched a campaign to recapture areas controlled by the Houthis, recovering ground near the Bab el-Mandeb Strait, a global shipping artery.
Residents of Taiz, northwest of Aden, have said they face intensifying bombardment and dwindling supplies as the Houthis tighten their grip on areas around the city, Yemen's third-largest.
War broke out in Yemen in 2014 when Houthi fighters seized the capital Sanaa, driving the government south.
A Saudi-led military intervention the following year led to a bloody stalemate before a 2022 truce that held until this year.
In that phase of the conflict Houthi fighters and allied forces briefly seized al-Maashiq palace during a battle for Aden before withdrawing.
