The incident occurred roughly at 05:30 p.m. local time in Police District 1 of the city after a suicide bomber approached and detonated his explosive vest near a vehicle carrying a former Afghan Local Police (ALP) official, the report said.
It was not immediately known if the official was hurt in the blast.
The wounded were shifted to a regional hospital in the city, which is the capital of western Herat province.
Those among the injured were several children. Earlier reports said two police were killed in the attack.
No group has claimed responsibility for the attack. The provincial officials blamed Taliban militants.
The Taliban-led insurgency has been on the rampage since the beginning of 2015 when Afghan security forces assumed full responsibilities of security from the U.S. and NATO troops.
On Tuesday night, nine ALP personnel were killed and one other injured after Taliban attacked a security checkpoint in Pashtum Zarghon district of the province.
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