Staff at the state-owned Commercial Bank of Ethiopia did not immediately spot the problem and, by the time it was noticed and halted, some $40 million (€36.7 million) had left the building.
Bank boss Abe Sano revealed the loss to local journalists as he reported that much of the money had been taken out by students through their CBE accounts.
News of the glitch, which happened last Saturday, was spread via WhatsApp and other chat groups.
Computer says 'yes' to students
University students formed long queues at campus ATMs as they rushed to withdraw money, only stopping when police officers arrived to intervene.
Ethiopia's central bank, which oversees the country's financial sector, said the glitch had happened during routine "maintenance and inspection activities" while CBE president Sano stressed it was not a cyber-attack.
Customer accounts were not affected and there was no cause for alarm, he added.
Some universities have urged their students to return the money but, so far, it is not known how successful that appeal has been. CBE says anyone returning the money will not need to fear criminal charges.
The bank, set up more than 80 years ago, has more than 38 million customers.
