A spokesman for Yemeni southern forces said al-Anad airbase was targeted with armed drones and missiles.
He blamed the Iran-aligned rebel Houthi movement, which is fighting a war against the Saudi-backed government.
The Houthis have not yet commented on the reports, but they have attacked the same airbase in the past.
Yemen has been devastated by a conflict that escalated in 2015, when the Houthis seized control of large parts of the country and a Saudi-led coalition launched an operation to restore President Abdrabbuh Mansour Hadi's rule.
The fighting has reportedly left more than 130,000 people dead and triggered what the UN says is the world's worst humanitarian crisis, with 12 million people reliant on food aid and half of children under five facing malnutrition.
A soldier who witnessed what happened at al-Anad on Sunday said he and his comrades were gathered inside a hangar after breakfast when they saw a drone hovering overhead.
"We tried to fire at it and bring it down, but we couldn't hit it," he told AFP news agency. "The craft flew over and headed directly towards the hangar, where it fired two missiles."
Another solider who was wounded in the attack, Nasser Saeed, told the Associated Press that 50 troops were inside the hangar when it was hit by missiles and bomb-laden drones, and that they shot one of them down.
Southern forces spokesman Mohammed al-Naqeeb said at least 30 soldiers were killed and 60 others were wounded, many of them critically.
He warned that the death toll might rise as rescue teams were still searching through the site.
President Hadi expressed condolences to the families of those killed and promised that the Houthis would "pay heavily for all the crimes they have committed against the people of Yemen".
In January 2019, six soldiers were killed in a Houthi drone strike on al-Anad, which occurred while high-ranking officers were watching a parade.