The clinic in the Somaa district of Al-Baida province was where the dentist worked before his execution, a local official told AFP.
The militant shot Motthar al-Youssoufi, then crucified his body and left it outside the health center on August 15.
On Tuesday, they blew up the clinic.
Al-Qaeda in the Arabian Peninsula (AQAP), which is active in Yemen, is considered the radical group's most dangerous branch.
The extremist group has thrived in the chaos of a Saudi-led war against Yemen.