The suicide bomber was on foot and targeted the army vehicle in Dahdadi district, said Munir Ahmad Farhad, spokesman for the provincial governor in Balkh.
He said another 18 military personnel were wounded in the attack, the Associated Press reported.
Taliban spokesman Zabihullah Mujahid claimed responsibility for the attack in an email to media. Taliban insurgents have intensified their attacks across the country against Afghan security forces in the year since the international combat mission wound down.
In eastern province of Nangarhar, a presidential palace guard was killed by unknown gunmen, said Attaullah Khogyani, spokesman for the provincial governor.
Khogyani added that the man was shot inside his house and his mother was also wounded in the attack.
"An investigation is underway by police to find out who is behind this attack," Khogyani said.
The chaos of Afghanistan's war, now in its 15th year, often masks criminal behavior and personal feuds.