Eighteen people were taken to hospital with injuries.
The bomber, who was riding a motorcycle, set off his explosives at the entrance to the city's central Blue Mosque.
Herat had been generally peaceful until today's attack, despite an upsurge in violence in other parts of Afghanistan.
Earlier in the day, four Canadian soldiers serving with NATO were killed by a suicide bomber in southern Afghanistan.
The attack took place near the Panjawayi district of Kandahar Province, an area where NATO on September 17 declared an end to a two-week-long offensive against Taliban militants.
Afghan police say the bomber rode a bicycle and detonated his explosives as the soldiers were distributing notebooks and pens to a crowd of Afghan children. At least 24 children were injured by the blast, four of them seriously.
In another suicide attack on September 18, at least one Afghan police officer was killed when a bomber targeted a market in eastern Kabul.