Blasts were heard at the city's eastern entrance near the Taizz airport, eyewitnesses said.
According to witnesses, anti-aircraft guns opened fire on the fighter jets.
No information is yet available about casualties.
Fractious Yemen has remained in turmoil since last September, when the Shiite Houthi militant group overran capital Sanaa, from which they have sought to extend their influence to other parts of the country.
Since last Wednesday, Saudi Arabia and its Gulf allies have pounded Houthi positions across the crisis-hit country.
Riyadh says the strikes are in response to appeals by embattled President Abd Rabbu Manshour Hadi to "save the [Yemeni] people from the Houthi militias."
Some Gulf countries accuse Shiite Iran of supporting Yemen's Houthi insurgency.