"One explosion occurred at morning rush hour in Police District 2 of the city, killing two children and injuring eight civilians passersby. The blast was aiming at terrorizing people and it caused panic among the residents," provincial police spokesman Adil Shah Adil told Xinhua.
Police and the rescue team reached the site after the attack was reported.
The second blast came about 20 minutes later, targeting the responding police and one police officer was injured, he said.
The dead and wounded were shifted to a nearby hospital, the police official added.
The initial investigation found the blasts were caused by two improvised explosive devices planted by militants.
No group has claimed responsibility for the attacks yet.
The province has been the scene of clashes between security forces and Taliban militants. Earlier this month, eight security force members lost their lives in a Taliban attack in Balkh.