The EBA urged users to "exercise the same caution with your digital wallet as you would do with your conventional wallet or purse."
The watchdog said people should not keep large amounts of money in their digital wallet for an extended period.
The warning comes as Chinese speculators have seen Bitcoin values plunge, soar and plunge again within days.
China is the world's biggest market for trading Bitcoins, but around $5.0 billion was wiped off the value of the currency's global stock within an hour of an announcement from Beijing's central bank in early December, banning financial institutions from dealing in it.
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Bitcoin was invented in the wake of the global financial crisis by a computer scientist using the pseudonym Satoshi Nakamoto. It is based on cryptography and only 21 million units can ever be created, which can be stored either virtually or on a user's hard drive.
It offers a largely anonymous payment system with no centralised structure and transactions are publicly l