A Reuters witness saw nine bodies on the ground after an explosion hit a military camp belonging to Yemeni forces backed by the United Arab Emirates, which is a member of the Saudi-led military coalition battling the Houthis.
A pro-government military source said a commander was among those killed.
"The blast occurred behind the stand where the ceremony was taking place at Al Jalaa military camp in Buraiqa district in Aden," the witness said. "A group of soldiers were crying over a body believed to be of the commander."
The Houthi's official channel Al Masirah TV said the group had launched a medium-range ballistic missile and an armed drone at the parade, which it described as being staged in preparation for a military move against provinces held by the movement.
The parade "was being used to prepare for an advance on Taiz and Dalea", Masirah cited a Houthi military spokesman as saying.
In a separate attack in another district of Aden on Thursday, an explosives-laden car blew up at a police station killing three soldiers, a security source said.
It was not clear if the incidents were related. Previous car attacks in Yemen have been carried out by Islamist militant groups like Al Qaeda.The Sunni Muslim coalition intervened in Yemen in 2015 to try to restore the internationally recognized government ousted from power in the capital Sanaa by the Houthis in late 2014. The Houthi movement says its revolution is against corruption.