Saleh, who has faced nationwide protests against his rule for the past four months, was "lightly wounded in the back of his head," a leader of the ruling General People's Congress (GPC) party told AFP.
His regime blamed the attack on powerful dissident tribesman Sheikh Sadiq al-Ahmar, whose fighters have been battling government forces in the Yemeni capital since a truce crumbled on Tuesday.
"The Ahmar (tribe) have crossed all red lines," GPC spokesman Tariq al-Shami said.
In an audio statement broadcast late Friday on state television, Saleh who was being treated at the defence ministry hospital in Sanaa said, "I am well, in good health," and added that the bombardment had killed seven people.
Saleh, who has been in power in Sanaa since 1978, hit out at "the sons of Al-Ahmar," a reference to Sheikh Sadiq and his brothers, and called on "the security forces to purge state institutions of these gangs."
The attack reportedly killed three officers of the elite Republican Guard.
Prime Minister Ali Mohammed Mujawar also suffered burns to his face, while a source close to the presidency said deputy premier General Rashad al-Alimi was "critically wounded."