Fighters attacked the patrol in Panjwal district, west of Kandahar, on Saturday. Nato had earlier said that the district was clear of Taliban fighters after a two-week offensive last month.
"One of the soldiers was wounded and later died of injuries sustained. One vehicle was also damaged," Nato said.
Saturday marks the fifth anniversary of the beginning of the offensive that swept the Taliban from power.
In a separate incident, two German journalists were shot dead by unidentified fighters in the north of the country.
A man and a woman, working for Deutsche Welle, were shot in their tent in the province of Baghlan.
Zemarai Bashary, an interior ministry spokesman, said: "They were killed by unidentified people in their tent... They were shot dead with AK-47s."
Also Saturday, a suicide car-bomber attacked a Nato patrol in the eastern province of Khost. The bomber was killed in the blast and no troops were hurt, a force spokesman said.
It was the third suicide attack in Khost since Nato took command of the province and the rest of the east from a US-led coalition force on Thursday.
More than 140 foreign troops have been killed since January, fanning opposition among the public and opposition parties in some Nato countries to their troops' involvement in Afghanistan.
After Nato's two-week operation against the Taliban in Panjwal, General David Richards, commander of Nato's Afghan force, said the Taliban had probably suffered its greatest single defeat since 2001.
A Nato commander said about 1,000 Taliban had been killed. The Taliban said casualties had been far fewer.