The deaths in the attack on Sardar Daud Khan Hospital, a health facility for wounded army soldiers, has gone up to 30 while at least 70 others were wounded, Tolo News quoted sources in the Ministry of Defense.
The attack ended around 4 p.m. (local time) after the three attackers were gunned down by security forces.
While the Taliban denied any involvement, the IS claimed responsibility for the attack.
The first blast took place around 9 a.m. at the military hospital in Wazir Akbar Khan area, where several government agencies and embassies are located.
A suicide bomber detonated his explosives at the main gate of the hospital. Later, four more attackers entered the hospital premises and then another blast took place.
The third bombing came around 10.45 a.m. when army helicopters were hovering over the building.
At least five suicide bombers were involved in the attack. One terrorist was killed in the bombing and two others were shot dead by security forces.
President Ashraf Ghani said the attack "trampled all human values".
"In all religions, a hospital is regarded as an immune site and attacking it is attacking the whole of Afghanistan," Ghani said, the BBC reported.
"I saw one of the suicide bombers who wore the doctors' uniform and opened fire. I managed to escape from the area," a doctor told Tolo News.
Afghanistan's Chief Executive Officer Abdullah Abdullah also condemned the attack and vowed to "avenge the blood of our people".
Meanwhile, the NATO-led Resolute Support coalition forces said they "stand ready to assist Afghan security services".
The 400-bed hospital, which is located in the diplomatic district near the US embassy, is the main and largest army hospital in the country.