The blast occurred just before 8 a.m. in Dehdadi district, not far from the Balkh provincial capital of Mazar Sharif, according to a statement by the Ministry of Defence, Reuters reports.
The ministry put the number of wounded at eight, while Munir Ahmad Farhad, a spokesman for the Balkh provincial governor, said that 14, including three women, had been injured.
"A suicide bomber attacked a bus which was carrying Afghan army personnel in this area. Unfortunately three army personnel were martyred and 14 others are wounded. The latest information we received from hospital indicates that 4 of those wounded are in critical condition." said Munir Ahmad Farhad, spokesman for Balkh provincial governor.
The bomber detonated a suicide vest near the bus as it was carrying members of the army's 209th Shaheen Corps, and all of the reported casualties were army employees, Farhad said.
The Taliban claimed responsibility for the bombing in a statement released online. The statement named a resident of Wardak province, which neighbors the Afghan capital city of Kabul, as the attacker.
Buses carrying military and government employees to and from work have been common targets for insurgent groups like the Taliban.