The incident comes a week after officials alleged that a woman accused of adultery was flogged and executed in the northwestern Badghis province.
Amnesty International has condemned the latest executions.
"The stoning of this couple is a heinous crime. The Taliban and other insurgent groups are growing increasingly brutal in their abuses against Afghans," Sam Zarifi, the rights group's Asia-Pacific director, said in a press statement.
"Afghan leaders must stand against stoning and other appalling human rights abuses masquerading as 'justice', no matter how much pressure they are under to deal with the Taliban."
On Monday, a spokesman for Nato-led forces criticised the Taliban for carrying out what he said were acts of indiscriminate violence against ordinary Afghans.
"They have increased acts of violence and repression against innocent Afghans," Brigadier General Josef Blotz told reporters.
"The insurgents have clearly given up winning over the population, knowing that they don't have an appealing vision for the people."