The four young children were killed in an attack in Herat.
The Taliban claimed responsibility for the Kandahar attack where the vehicle the UN workers were travelling in was almost completely destroyed by the powerful explosion from a remote-controlled bomb.
A United Nations spokesman said the vehicle from the United Nations Office for Project Services (UNOPS) had been attacked while travelling to the UN's base in Kandahar city.
"The blast has claimed the lives of an Afghan driver and four Nepalese contractors working with the UN office for project services," the UN said in a statement released from the capital Kabul.
Kandahar is the birthplace of the Taliban, the main movement that is opposed to the UN-backed government in Kabul, the capital of Afghanistan.
Taliban threaten more attacks
Qari Yusuf Ahmad, a Taliban spokesman, told Al Jazeera that fighters from his group had carried out the attack on the UN convoy
Another Taliban commander, Mullah Hayatullah Khan, separately told the Reuters news agency that his fighters would continue to attack people helping foreign forces in Afghanistan.
"We'll target all individuals or organisations that are either co-operating with coalition forces or working under their supervision," Khan said, speaking by satellite telephone from an undisclosed location.
Violence in Afghanistan surged last year to its worst level since the Taliban were ousted 2001, killing around 4,000 people.