The blast occurred in Paktika province Friday when their vehicle hit a pressure-plate improvised explosive device planted on a public road, the UN said, adding that four others were wounded.
"Children are once again the main victims of these indiscriminate and illegal weapons," said Pernille Kardel, the UN's deputy special representative in Afghanistan.
"There is a simple message to the perpetrators: stop using these weapons if you are serious about safeguarding Afghanistan's civilians and the country's future generation," Kardel said in a statement on Saturday.
There was no immediate reaction from officials in Paktika, AFP reported.
The bombing comes just days after the UN voiced alarm over the killing of 25 civilians in the escalating conflict in southern Helmand province, most of them in US airstrikes.
An American bombardment in Helmand's Sangin district last week killed 18 people, nearly all women and children, the UN said.
Afghan civilian casualties in 2016 were the highest recorded by the UN, with nearly 11,500 non-combatants killed or wounded.
More than 3,500 children were among the victims, a "disproportionate" increase of 24 percent in one year, the UN said in a report earlier this month.
Afghanistan last year also saw the highest recorded civilian casualties caused by pressure-plate IEDs in a single year, the world body said.