More than 38 million people hold accounts at Commercial Bank Ethiopia
The customers discovered early on Saturday that they could take out more cash than they had in their accounts at the Commercial Bank of Ethiopia (CBE).
More than $40m (£31m) was withdrawn or transferred to other banks, local media reported.
It took several hours for the institution to freeze transactions.
Much of the money was withdrawn from state-owned CBE by students, bank president Abe Sano told journalists on Monday.
News of the glitch spread across universities largely via messaging apps and phone calls.
Long lines formed at campus ATMs, with a student in western Ethiopia telling BBC Amharic people were withdrawing money until police officers arrived on campus to stop them.
The student, who attends Jimma University Institute of Technology, said he "did not believe it was true" when his friends told him at around 01:00 local time (22:00 GMT) that it was possible to withdraw large amounts from ATMs, or transfer the money using the bank's app.
Another student, at Dilla University in southern Ethiopia, said a number of his peers retrieved money from CBE between midnight and 02:00 local time.
More than 38 million people hold accounts at CBE, which was established 82 years ago.
Ethiopia's central bank, which serves as the financial sector's governing body, released a statement on Sunday saying "a glitch" had occurred during "maintenance and inspection activities".
The statement, however, focused on the interrupted service that occurred after CBE froze all transactions. It did not mention the money withdrawn by customers.
Mr Sano did not say exactly how much money was withdrawn during Saturday's incident, but said the loss incurred was small when compared to the bank's total assets.
He stated that CBE was not hit by a cyber-attack and that customers should not be worried as their personal accounts were intact.
At least three universities have released statements advising students to return any money not belonging to them that they may have taken from CBE.
Anyone returning money will not be charged with a criminal offence, Mr Sano said.
But it's not clear how successful the bank's attempts to recoup their money has been so far.
The student from Jimma University said on Monday he had not heard of anyone giving the money back, but said he had seen police vehicles on campus.
An official at Dilla University said bank employees were on campus collecting money that some students were returning voluntarily.
-- Courtesy of BBC News