The reason for the fatal shootings on August 11 is not yet clear, but local Afghan authorities said they have asked Iranian officials for an explanation.
The Afghan Foreign Ministry has said it is investigating the matter, while Iran has yet to make any official comments.
RFE/RL's Radio Free Afghanistan reports that the incident set off angry protests in Herat.
Relations between Iran and Afghanistan were strained earlier this year by Tehran's forcible repatration of tens of thousands of Afghan refugees.