The explosion took place as worshippers were praying at a mosque used by Saudi special forces in Abha, the broadcaster said, describing it as a “terrorist” attack. It gave no further details.
An interior ministry spokesman confirmed the attack but gave a slightly lower toll of “more than 13” dead.
The victims were members of a Special Weapons and Tactics (SWAT) unit, the spokesman told AFP.
“It’s confirmed there’s an explosion and there’s more than 13 (killed)… in a mosque,” the spokesman said.
The explosion happened at the headquarters of the SWAT team, which is tasked with domestic security, he added.
It was too early to say who may have carried out the attack, he added.
Saudi Arabia has been on alert for attacks by the jihadist Islamic State group, who have been blamed for killing policemen and for slaughtering members of the minority Shiite community.