As per reports, the explosions took place when President Ashraf Ghani was speaking live on television on the occasion of festival Eid-Al-Adha.
As per AFP, at least nine rockets hit near the diplomatic area in the city. BBC reported that some of the explosions took place near the presidential palace as well.
Ghani had called for an Eid ceasefire which was dismissed by the militant group.
Smoke and helicopters were witnessed above Eidghah Mosque in Reka Khana district, AFP reported.
Heavy security was deployed near the Kabul Stadium.
Smoke and helicopters could be seen above the Reka Khana district, an AFP news agency photographer said.
The agency quoted interior ministry spokesperson saying that a group of terrorists took over a building in Reka Khana and fired several rockets towards Kabul. He said two people have been injured and the fight between security forces and militants is underway.