The Emergency Hospital in Kabul said in a tweet that at least 20 wounded were brought to their surgical centre after the explosion. Television pictures showed numerous injured suffered serious burns.
In a statement Thursday, President Ashraf Ghani called the attack "inhumane" and against the tenets of Islam.
The Islamic State group claimed responsibility for that explosion.
Kabul has been hit hard by terror attacks attributed to Taliban, Islamic State (IS), and other militants operating in the country. Before that, there had only been one major attack, in 2011. The bomber blew himself up inside a Shi'ite Muslim cultural center in the city.
Backed by the heaviest USA air strikes since the height of the global combat mission in Afghanistan, Afghan forces have forced the Taliban back in many areas and prevented any major urban center from falling into the hands of insurgents.
"This gruesome attack underscores the dangers faced by Afghan civilians", rights group Amnesty International said in a statement from its South Asia Director, Biraj Patnaik.
There has been an increase in security since last May when a truck bomb in the diplomatic quarter killed 150 people and wounded around 400 others.
Police officers at the scene said the bomber had been wearing police or army uniform and had approached a group of security personnel conducting controls on illegal drugs and alcohol sellers, but there was no official confirmation.
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