Khan Muhammad Khan, the chief of police for Kandahar province, said the attack occurred on Sunday evening on the approach to a bazaar in Maywand district, 65km west of Kandahar city.
He said three of the fighters escaped, but one was killed after police returned fire.
On Saturday, two US soldiers were wounded when their patrol came under attack from small arms fire at Shinkay, about 50km northeast of Qalat, the main city of Zabul, a province neighbouring Kandahar.
Both soldiers were in a stable condition and would be sent to Germany for treatment, Major Mark McCann of the US army said in Kabul.
The 18,000-strong US-led force in Afghanistan began Operation Lightning Freedom last week to keep up the pressure on anti-government fighters over the winter, to prevent them from regrouping as they had in past years.
The US forces, along with an 8400-strong Nato-led peacekeeping force, aim to minimise the threat from insurgents to a parliamentary election due in April after last October’s successful presidential poll.