0830 GMT July 16, 2018
The blast occurred in Kabul's Karte Sakhi area close to the Ali Abad hospital and Kabul University on Wednesday, Press TV wrote.
The Afghan Interior Ministry said at least 26 people had been killed and 18 injured in the attack.
Reports said many of those killed were Shia and the casualty toll could still rise.
The bomber reportedly walked toward the Sakhi shrine and blew up his explosives when identified by the police.
The Daesh terror group claimed responsibility for the attack.
At least three civilians were also killed in the Afghan capital on Saturday in an attack, during which an assailant blew up a bomb-laden vehicle.
The Saturday attack came amid talk of possible direct dialog between the Taliban and the Afghan government or between the militant group and the United States.
The explosion also comes two days after the top commander of US forces in Afghanistan, General John Nicholson, said protecting Kabul was "our main effort."
Nine people were also killed and 18 others injured in a bomb attack near a Shia mosque in Kabul earlier this month.
The casualties were caused after an attacker, who had been stopped at a nearby security checkpoint, set off an explosive device he was carrying, said Nasrat Rahimi, a deputy Interior Ministry spokesman.
It came a few days after a fatal car bomb attack hit near foreign diplomatic missions and government buildings in the heart of the Afghan capital.
According to witnesses and officials, an ambulance laden with explosives went off at a police checkpoint near an office of the High Peace Council and a number of foreign diplomatic missions.