Customers discovered early on Saturday that they could withdraw more cash than they had in their accounts at the Commercial Bank of Ethiopia (CBE).
According to local media reports, more than $40 million was withdrawn or transferred to other banks.
It took several hours for the institution to freeze transactions.
Bank president Abe Sano told reporters on Monday that the bulk of the money was withdrawn by students from the state-owned CBE.
News of the problem spread to universities largely through messaging apps and phone calls.
Long lines formed at campus ATMs, and one student in western Ethiopia described Amharic people withdrawing money until police officers arrived on campus to stop them.
The student, studying at Jimma University's Institute of Technology, said he "didn't believe it was true" after friends told him at around 1 a.m. local time that it was possible to withdraw large sums of money from ATMs.
More than 38 million people have accounts at the CBE, which was founded 82 years ago.
Ethiopia's central bank, which serves as the governing body of the financial sector, issued a statement on Sunday saying "a glitch" had occurred during "maintenance and inspection activities".
At least three universities have issued statements advising students to return money they may have received from the CBE that does not belong to them.
Sano said no one who returns the money will be charged with a criminal offense.
