The explosion occurred at 4:06 p.m. local time (1136 GMT) in Wazir Akbar Khan area, a fortified diplomatic enclave in Kabul.
Dawlat Waziri said the explosion occurred near the USA embassy and the Afghan defense ministry.
The death toll in a suicide bombing attack in Afghanistan's Green Zone on Tuesday has mounted to nine. The attack in 14th Street in Wazir Akbar Khan area inside the Green Zone claimed the lives of 13 persons.
The Health Ministry confirmed that at least five people, mostly government employees, had died and almost 30 others were injured, the Afghan media reported.
Islamic State claimed responsibility for the attack.
Police cordoned off the area immediately after the blast.
Security had already been stepped up considerably following a devastating truck bomb attack outside the German embassy on May 31 that killed at least 150 people, with a series of barriers and checkpoints across the central area of the city.
A defence ministry spokesman told Al Jazeera that the blast happened outside their building.
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