The Reserve Bank of Zimbabwe said it was investigating CBZ after it allowed one customer to withdraw $44 180.
Ecobank allowed a customer to withdraw $15 000. It is also under investigation.
The normal withdrawal limit is $300 a week.
Zimbabwe is facing a serious cash crisis which the government is trying to address by injecting cash into the market.
The shortage has led to a thriving black market. Those with cash are trading electronic money at huge discounts.
Cash is also required to purchase United States dollars which have become a store of value though Zimbabwe has declared the local currency the sole trading currency.