The convoy was made up of a prison van and a police vehicle.
The prison van carried 14 policemen and 20 inmates, while the police vehicle carried civilians of eight men and two women.
The 10-member AA group attacked the convoy by setting off two remote-controlled mines on Thursday afternoon on Buthidaung-Maungtaw road in Buthidaung township.
The policemen escorting the prison van returned fire, forcing the AA members to retreat.
The inmates were sent to the Buthidaung Prison and the security forces are conducting security measures around the site of the attack, police added.
On Aug. 20, AA launched similar mine attack on a police convoy on Yangon-Sittway road in the same state, killing three police members and injuring three others.
Arakan Army (AA) is a Rakhine rebel group fighting for the rights of ethnic Rakhine people in Myanmar. It usually fights alongside the Kachin Independence Army (KIA) against the Myanmar Armed Forces.