The civilians died when an improvised bomb placed on an abandoned bicycle was remotely detonated near a convoy of trucks supplying foreign forces in the city of Ghazni, south of Kabul, police said.
A passer-by was injured in the blast, Khyal Baz Sherzai, the provincial police chief, told AFP. He blamed the attack on Taliban insurgents.
A police officer was killed while defusing a roadside bomb in Kandahar, another troubled city in the south, the interior ministry and a local police official said.
"He was trying to defuse the bomb. It was a Taliban bomb," a local police official told AFP at the site of the blast.
Separately, the defence ministry said Afghan troops killed two insurgents in a gunbattle elsewhere in Ghazni. The fighting erupted after the rebels attacked troops patrolling the area.
Violence from a Taliban-led insurgency has surged in recent weeks, claiming the lives of dozens of international soldiers and civilians.
Thousands of US Marines and British troops backed by Afghan security forces have been battling their way into some of the most dangerous Taliban strongholds in a massive push against the rebels.
The operations have been designed to drive Taliban and other insurgents from the southern province of Helmand in the run-up to presidential elections on August 20.