Five women, five children and a man in a vehicle were killed in Logar province on Friday.
Stanikzai said the family had been on their way to a wedding when the explosion occurred.
Those among the killed were five women and five children. The Provincial Governor said 10 Taliban fighters were also killed, including two commanders.
Violence has been on the rise as Afghan security forces struggle against a surge in attacks by the Taliban since the drawdown of foreign forces over the past two years.
Earlier, a policeman turned his rifle on his colleagues as they slept at an outpost in eastern Nangarhar province on Thursday night, also killing five.
No group including the Taliban insurgents or any other terrorist group has so far claimed responsibility behind the incident.
Provincial governor's spokesman Ataullah Khogyani confirmed the incident and said the policemen were killed by one of their comrades on Thursday night. The blast disabled an armored vehicle but caused no injuries.
A roadside landmine claimed 11 lives of a family in southeastern Afghanistan on Friday, APA reports quoting Anadolu Agency.
He added that after the shootings, the attacker, whose name was only given as Nasratullah, collected his victims' firearms and fled the scene.
Without sharing more details, a US military spokesman told VOA "the disabled vehicle is being recovered and the convoy will continue and complete its mission".