Security officials have confirmed at least 14 rockets were fired off and landed in different parts of the city, including in the diplomatic zone and close to the Presidential Palace.
Widespread damage to buildings and vehicles was also reported and at least 10 people were wounded.
According to Tariq Arian, an interior ministry spokesman, the rockets had been fired from two vehicles.
“Unfortunately, 10 civilians including four children and one woman have been wounded.”
He confirmed at least 14 rockets landed in the city and that two people had been arrested.
“Most of these rockets have hit civilian houses in Kabul,” Arian said.
No group has yet claimed responsibility for the attack.
However, it did not stop officials from holding ceremonies in other provinces, including Nangarhar, Herat and Kandahar and messages wishing Afghanistan a Happy 101st Anniversary of Independence poured in from around the world.
Saudi Arabia’s King Salman bin Abdulaziz Al Saud was one person who congratulated Ghani and the people of Afghanistan on the occasion.
According to the Saudi Press Agency, the king “wished the President constant good health and happiness and the Government and people of the Islamic Republic of Afghanistan security and stability.”
Resolute Support Commander General Scott Miller meanwhile posted a video on Twitter and used the opportunity to call for a reduction in violence.
He said: “I’d like to wish the people of Afghanistan a happy Independence Day. We stand behind your ANDSF security forces as they secure peace in Afghanistan.
“Now is the time to reduce violence and build a political path towards peace.
The United Nations also wished Afghanistan well and said it was “sharing the hope that the year ahead will witness a breakthrough in peace efforts and the forging of a peaceful and prosperous Afghanistan.”
In a statement issued on Tuesday by the Taliban, the group acknowledged the country’s day of independence but said that as their forefathers responded to “the invading enemy”, they too will continue their fight.
“… we too shall continue our comprehensive struggle with all our might towards regaining our sovereignty and establishing an Islamic government in our homeland and shall not allow anyone to stand in the way of this great and pure aspiration, Allah willing.”
Afghan Independence Day is celebrated as a national holiday in Afghanistan on 19 August to commemorate the Anglo-Afghan Treaty of 1919 and relinquishment from protected state status.
The treaty granted a complete neutral relation between Afghanistan and Britain.