The incident occurred on Wednesday in the Hasankhail area, Mezan district of Zabul, when the bombs hit houses rather than suspected positions of the Taliban fighters, the Bakhtar news agency said citing a local police chief.
The injured civilians were admitted to Qalat Hospital in stable condition.
Afghanistan, where the hard-line Islamic Taliban regime was overthrown in a 2001 U.S.-led campaign, has seen a rise in violence in recent years.
Last year was the deadliest in Afghanistan since 2001. According to UN reports, more than 8,000 people died in insurgency-related violence, including more than 1,500 civilians.
NATO maintains a 47,000-strong peacekeeping contingent in Afghanistan and is planning to send more troops to the conflict-stricken area.
On April 4, Russia and NATO agreed on land transits for non-lethal freight through Russian territory to NATO troops deployed in Afghanistan.
