There were no immediate reports of casualties after the rockets were fired from two vehicles in Kabul, interior ministry spokesman Tareq Arian said.
The rockets struck the capital after President Ashraf Ghani participated in an independence day ceremony at the presidential palace.
Witnesses said some rockets fell near the palace and the defense ministry in a heavily fortified area that also houses several embassies, Arab News reported.
The rocket attack comes as the Afghan government and the Taliban are poised to begin peace talks.
Negotiations are set to start once Kabul completes the release of some 400 Taliban prisoners as approved last week by a traditional gathering of prominent Afghans.
Ghani’s swearing-in ceremony on March 10 was interrupted by rocket fire near the palace. No serious injuries were reported at the time.
Afghanistan was never a part of Britain’s empire but it became fully independent from British influence in August 1919.