The Co-operative Bank failed a "stress test" that assesses major UK lenders' ability to withstand an economic crisis in the UK.
Lloyds Banking Group and Royal Bank of Scotland are a further two banks that were found to be at risk if there were another financial crisis.
The lenders' resilience was tested against a 30% drop in the value of the pound and a 35% fall in house prices, among other factors.
Five major banks passed the test including HSBC, Barclays, Santander, Standard Chartered and Nationwide.
The EBA found that 24 European banks needed to shore up their finances.
Four UK banks were subjected to the EBA test: Royal Bank of Scotland, HSBC, Lloyds Banking Group and Barclays. They all passed.