More than 40 people were also reported to have been injured in the attack in the city of Kunduz.
On Friday, the Kunduz province police chief was killed by a suicide bomber.
Over the last few years, the once peaceful province has become increasingly unstable as the Taliban have infiltrated the area.
People were waiting in the recruitment centre when the attack took place, a senior official told the BBC's Bilal Sarwary.
Those killed included civilians - some of them women and children - as well as men who had come to enrol, and officers in the Afghan army, he said.
A doctor in a hospital in Kunduz has told the BBC he had received 33 dead bodies and that some of the injured were in a very serious condition.
It is not the first time the recruitment centre has been attacked, says the BBC's Quentin Sommerville in the capital, Kabul.
This attack comes four days after the provincial police chief of Kunduz, Abdul Rahman Sayedkhili, was killed by a suicide bomber on a motorcycle in the city, along with four other people. The Taliban say they carried out the attack.
And last month, 30 people died in another suicide bombing in the city.
The Taliban have been warning Afghans not to allow their sons and brothers to join the country's security services.
The police and army are undergoing a rapid expansion as they prepare to take control from foreign forces, due to end ther combat operations in Afghanistan in 2014.
The United Nations has said the insurgents have changed their tactics and are now increasingly targeting civilians, in an effort to hinder the transition of power in the country, our Kabul correspondent adds.