The strikes followed the fall of the base outside Taiz of an army unit loyal to President Abdrabbuh Mansour Hadi.
Fighting was also reported in the second city of Aden, Lahj’s provincial capital Huta, and the town of Daleh.
On Tuesday, Riyadh declared its month-long campaign, which sought to restore the president.
But it warned that it would continue to take action against the Houthis as needed.
More work “needs to be done” in Yemen, US White House spokeswoman Jen Psaki told CNN, while emphasising the need for a negotiated solution.
Yesterday the Houthi rebels asked for the coalition action to end and for UN-sponsored peace talks.
The UN says at least 944 people have been killed and 3,487 injured in air strikes, fighting on the ground and attacks by jihadist militants in Yemen since March 19.