The incident took place at around mid-day when thousands of people were holding a demonstration against change in the route of a major electricity line.
The number of the casualties may further go up as several wounded remained in critical condition, he said.
The explosion also shattered the windows of nearby buildings and houses.
Dehmazang Square was announced by the demonstrators as the center of their protest after they were prevented by security forces to march towards Pashtonistan Watt, an intersection in central Kabul near the countrys Presidential Palace.
The demonstration, held by the so-called "Enlightening Movement" protesters mainly from minority Hazaras, started on Saturday morning.
The protesters leaders were trying to set up tents and prepare the protesters to stay at night at the square before the deadly blast.
The nature of the blast still remained unknown. However, unofficial sources said the explosion was conducted by a suicide bomber.
Media reports said the Islamic State (IS) claimed responsibility for the attack. The Taliban militants denied involvement in the attack.
Afghan President Mohammad Ashraf Ghani and Chief Executive Abdullah Abdullah strongly condemned the attack and ordered the concerned authorities to provide best medical assistance to the victims of the deadly incident.