A spokesman for the governor of Laghman province, Assadullah Dawlatzai, said the blast outside the police headquarters partially destroyed a nearby religious school.
"The Students were injured by the explosion," he said, adding that "about 20" students were injured.
Six police officers were also injured.
The Afghan Interior Ministry confirmed the toll and accused the Taliban of being behind the bombing.
The Taliban has yet to make any statement.
Afghanistan is currently awaiting the results of the first round of presidential elections held last month.
There were limited attacks by the Taliban, which sought to disrupt the democratic process.