Mohammad Rahim Amin, chief of the Baraki Barak district in eastern Logar province, said the deaths and injuries occurred when Afghan soldiers opened fire on hundreds of protesters who were trying to storm the local government headquarters.
During recent protests against the Koran burning, Afghans have regularly targeted the pro-Western government.
The protesters in Logar chanted "Death to America" and burned tyres, attacked several shops and set election campaign posters on fire, Mr Amin said.
The imam leading an effort to build a mosque and Islamic centre near the World Trade Centre site in New York said the raging debate on whether it should be moved has stoked anti-Muslim feelings.
Imam Feisal Abdul Rauf said in a TV interview that the controversy over the mosque site has heightened concerns among Muslims of rising Islamophobia, and fear of Islam is possibly greater than it was immediately after the September 11 terrorist attacks.