BRUSSELS—The European Union’s banking watchdog said Bulgaria’s central bank and deposit insurance fund were breaching the bloc’s deposit-guarantee law by not allowing depositors to access their savings at Bulgaria’s Corporate Commercial Bank.

Monday’s recommendation by the London-based European Banking Authority comes after the watchdog opened an investigation last month into whether measures taken by Corpbank’s temporary management breached an EU law that requires depositors to be compensated for up to €100,000 ($127,851)...