A burst of gunfire was heard in the compound of the governor of the southern Afghan province of Kandahar soon after a meeting attended by Miller, witnesses and Afghan officials said.
The police commander of Kandahar, General Abdul Razeq, was killed, an aide said.
A NATO spokesman said Miller was uninjured but two other American citizens were wounded, Reuters reported.
Miller, who had been attending a meeting with security officials ahead of parliamentary elections on Saturday, was not injured but two Americans were wounded in the crossfire and had been evacuated, NATO spokesman Colonel Knut Peters said.