The family was driving through the Khanashin district Saturday when the vehicle triggered an improvised explosive device, Khaama Press reported Sunday.
The International Security Assistance Force condemned the attack, which it said was caused by insurgents.
"Our condolences go out to the loved ones impacted by last night's senseless violence." said Brig. Gen. Günter Katz, ISAF spokesperson in a statement. "An attack on any innocent Afghan civilian should be viewed as an attack on all Afghan people. Insurgents use these desperate and indiscriminate acts in an effort to slow the momentum of Afghanistan's progress toward a brighter future, but they will not prevail."
No group has come forward to claim responsibility for the roadside bomb, Khaama Press reported.