The explosion took place on Sunday when Bin Sultan’s deputy was entering the building, Yemen’s al-Fajr Press quoted eyewitnesses as saying.
Saudi media have so far refrained from showing any reaction to the blast. No official report has yet been released on the incident.
On Thursday night Prince Bandar bin Sultan was appointed Saudi Arabia’s new spy chief.
Prince Bandar, 63, who vanished from public view when he was recalled from Washington by King Abdullah in 2005 after notching up 22 years as the kingdom’s ambassador there, will immediately be thrust into a Middle East crisis.
The US’ closest Arab ally is a supporter of the Syrian rebels who want to oust President Bashar al-Assad.