Baida is a stronghold of the Sunni militant group.
The gunmen, who had concealed their identities, opened fire at Hussein Dayan outside his home in Baida's  provincial capital, the official told Agence France Presse (AFP).
"The attack bore the hallmarks of Al-Qaeda," he said.
Widely regarded as the most active and dangerous wing of the global jihadist network, Al Qaeda in the Arabian Peninsula (AQAP) use Baida's mountainous terrain to hide from security forces and launch attacks, according to AFP.
The militant group has racheted up its activities in Yemen since the central government became weakened in 2011 as a result of a popular uprising that saw president Ali Abdullah Saleh after 33 years in power, AFP reported.