His son Saif al-Arab was said to be killed, as well as three grandsons.
Journalists say the building was extensively damaged and one unexploded bomb remains at the site.
Saif al-Arab, who had a lower profile than his brother Saif al-Islam, had been studying in Germany and returned to Libya recently.
Government spokesman Moussa Ibrahim said the villa in which he was killed was attacked "with full power."
"The attack resulted in the martyrdom of brother Saif al-Arab Muammar Gaddafi, 29 years old, and three of the leader's grandchildren," he said.
"The leader with his wife was there in the house with other friends and relatives, the leader himself is in good health, he wasn't harmed." Col Gaddafi's wife was also unharmed, he said.
"This was a direct operation to assassinate the leader of this country," the spokesman added.
'Law of the jungle'
At the scene Christian FraserBBC News, Tripoli
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