The rockets landed near the presidential palace in the capital, Kabul, during prayers for the Muslim festival of Eid al-Adha, a live television broadcast showed.
There were no immediate reports of injuries, local media reports said on Tuesday.
The rockets, fired at around 8:00 am were heard across the heavily fortified Green Zone that houses the palace and several embassies, including the US mission.
“Today the enemies of Afghanistan launched rocket attacks in different parts of Kabul city,” said interior ministry spokesman Mirwais Stanikzai.
“All the rockets hit three different parts. Based on our initial information, we have no casualties. Our team is investigating.”
Minutes after the attack, Ghani began an address to the nation in the presence of some of his top officials.