The incident occurred at 8:15 local time when a suicide bomber driving a bomb-laden car tried to hit a diplomatic car belonging to the Turkish embassy while it was passing by the Iranian mission in the Afghan capital, IRNA reports.
The driver was killed, said Deputy Interior Minister of Afghanistan General Mohammad Ayoub Salangi.
However, no damage has been reported to be inflicted on the Iranian embassy and the site of the blast is under tight security measures.
The blast took place outside the gate of the Iranian embassy, which is adjacent to the Turkish mission in the centre of Kabul.
The Taliban claimed responsibility for the blast in a text message to media, saying that the target was a "convoy of foreigners' vehicles", Reuters report.
Associated Press television footage showed smoke rising from two black armoured vehicles bearing Turkish diplomatic plates.
It is the first known attack on a Turkish target in the Afghan capital.
No reporter is allowed to enter the area. Salangi told reporters that investigations are underway after the incident.
"The target was a Turkish embassy vehicle, one person is wounded and the driver possibly killed," he said.