A military spokeswoman said on Monday the casualties occurred when their Humvee drove on to a makeshift landmine in Zabul province near Deh Rawood.
"All three were taken to Kandahar airfield hospital where one soldier died," she added.
The incident comes as US-led occupation forces fight an escalating insurgency in the south and southeast - mountainous regions believed to be home to a permanent Taliban presence.
UN staff working on the forthcoming presidential elections survived a bold attack in southeastern Paktia province on Sunday when rebels attempted to ambush their four-vehicle convoy with two landmines and small-arms fire.
The 15 international and Afghan staff, who were being escorted by armed police, were unharmed.
The Paktia incident is the most serious of its kind since two Britons working on security for the polls were beaten and shot dead with their Afghan interpreter in eastern Nuristan a month ago.
A spokesman for the US military, which was called in to provide air support to the beseiged UN convoy, said the attack had been a "fairly protracted engagement".
The Taliban have regrouped in
Lieutenant Colonel Tucker Mansager said the US-led occupation force was working closely with the Afghan government and the UN to provide "a secure and stable framework for these democratic elections in September".
Aid workers at risk
Medecins Sans Frontieres, a medical aid group which lost three European and two Afghan staff in an ambush and shooting last week, said the occupation force's activities were putting aid workers at risk.
Actions such as distributing leaflets linking the provision of aid with cooperation with soldiers "create a misperception that humanitarian action is in service of someone's military or political cause", the group's director of Dutch operations Kenny Gluck said.
"It's spoiling the general environment for humanitarian action."
While it is not known who was responsible for the recent attacks, Taliban activists have threatened to disrupt the elections scheduled for September and warned Afghans against working with the electoral process.
Voter registration sites were open in each of Afghanistan's 34 provinces on Monday after a small number of booths started work in southeastern Paktia province.
"I can confirm voter registration sites opening in Nuristan yesterday (Sunday) and Paktia today (Monday)," electoral commission spokesman Muhammad Azam said. "This covers the whole country."
The main phase of voter registration began on 1 May but several provinces were initially excluded because of security concerns. So far three million of an estimated 10 million eligible Afghans have registered to vote.
However, electoral officials have raised concerns about the uneven geographical distribution of voters, with only a small proportion coming from the troubled south and southeast, and the slow pace of registration.
Violence and funds shortage may
yet derail Karzai's election plan
The US-backed government of President Hamid Karzai has stressed that elections will go ahead in September as planned, but fears are rife that the polls may be hurt by the ongoing insurgency and funding problems.
The presidential and parliamentary polls are projected to cost around $101 million. But despite large pledges, the United Nations, which is helping to organise the vote, has so far no received no money to pay for them.
While the international community has pledged $70 million, "not one penny is in the bank", a UN spokesman said on Sunday.
Meanwhile, anti-occupation attacks show no sign of abating.
In addition to the attack on the UN convoy on Sunday, suspected Taliban killed a policeman in a three-hour attack on a government headquarters in eastern Logar province.
US-led troops, who now number some 20,000 in the country, fought opposition fighters in Zabul and Uruzgan provinces on Thursday, Friday and Sunday in engagements which left at least 17 suspected Taliban dead.
Occupation forces captured five suspected rebel fighters after a firefight in the southeast Afghan border town of Spin Boldak on Friday.