At least one other child was injured in the blast.
There was no immediate claim of responsibility, but Bashary said the explosion was "an act of insurgents".
"This is the worst of brutality of the enemy," he said.
A day earlier, at least four US soldiers and more than a dozen other people were killed in separate incidents in eastern and northern Afghanistan.
Violence in Afghanistan has increased during the past three years to its highest level last year since the US-led invasion of the country in 2001.
Barack Obama, the US president, has said he is sending more than 20,000 additional soldiers to the country to suppress attacks.
The US entered the country to oust the Taliban, who they accused of harbouring al-Qaeda fighters, in the wake of the September 11, 2001, attacks.