At least one civilian and two members of the Afghan security forces were killed, a ministry spokesman said, adding that the target appeared to be a police post near military headquarters.
ISIL claimed responsibility in an online post.
A police officer at the scene told Reuters the attack appeared to have been carried out by a suicide bomber on foot. A Reuters witness reported seeing several damaged cars, with possible injuries to the occupants.
Last month, ISIL fighters killed nearly 50 people when they stormed the main military hospital in Kabul.
ISIL offshoot in Afghanistan is suspected of carrying out several attacks on minority Shiite Muslim targets. US officials say intelligence suggests ISIL is based overwhelmingly in Nangarhar and neighboring Kunar province.
Estimates of its strength in Afghanistan vary. US officials have said they believe the group has only 700 fighters but Afghan officials estimate it has about 1,500.
The Afghan Taliban, who are trying to overthrow the US-backed government in Kabul, are fiercely opposed to ISIL and the two have clashed as they seek to expand territory and influence.