Rockets landed near the Afghan presidential palace during morning prayers on the significant Eid el-Adha holiday, a live feed on Afghan television showed.
"Today, the enemies of Afghanistan launched rocket attacks in different parts of Kabul city," interior ministry spokesman Mirwais Stanikzai told AFP.
Rockets have been fired at the Afghan presidential palace in the past, most recently last December.
Unlike in previous years, the Taliban did not announce a cease fire to coincide with the Eid holiday this time.
Tuesday's attack comes hours after ceasefire talks between the Taliban and the Afghan government in Kabul in Doha broke down, despite the objections of 15 diplomatic missions and the NATO representative in Kabul.
The incident comes amid a deteriorating security situation, with the Taliban making gains across the country. Several rural districts have already fallen and are now controlled by the Taliban.
US and NATO forces are currently on schedule to complete their withdrawal from the country by August 31.