The projectile struck the third floor of the building near central Tripoli overnight, and an aide told reporters that Miitig was not in his office at the time.
Despite the attack, Miitig travelled to his offices today to hold a meeting with his ministers, an AFP journalist said.
Miitig, an independent backed by Islamists, had convened his first cabinet meeting on Monday despite the objections of outgoing premier Abdullah al-Thani, who refused to recognise his government.
State buildings in Libya are regularly targeted by rival militias. The central government in Tripoli has struggled to impose its authority since the ouster of dictator Muammer Gaddafi by a popular uprising in 2011.
Groups of former rebels who fought the Gaddafi regime have refused to surrender their weapons and still control swathes of territory across the North African nation.