Seven people were injured as a result of the blast, the ministry added.
The ministry spokesman Nasrat Rahimi said the bomb went off near the interior ministry and north of Kabul airport.
No group has taken responsibility for the attack.
The blast occurred even as Afghan President Ashraf Ghani announced on Tuesday that three Taliban prisoners would be released in a prisoner swap for two Western hostages.
The three Taliban prisoners include Anas Haqqani, who was arrested in 2014.
"We have decided to conditionally release three Taliban prisoners who... have been in Bagram prison in the custody of the Afghan government for some time," Ghani said in an announcement
Last week, an Afghan police officer and a terrorist were killed and four police officers sustained injuries in a suicide car bombing carried out by the Taliban at a military camp in southern Kandahar province.
Another attack had taken place in Afghanistan's Logar province in which four judges were killed.
Afghanistan has seen months of uncertainity even as it prepares to announce the results of the presidential polls which has been delayed for several weeks. The results of elections which had taken place on September 28 was due to be out on October 19 but slow work on data entry and tackling extensive voter fraud has delayed the announcement.
Eighty-five civilians were killed and more than 370 wounded in militant attacks and violence on the day of the election, the United Nations had said last month.
Ghani and Abdullah had both claimed victory before the ballots were tallied.