Swiss bank UBS will start charging customers who deposit more than a million euros, as negative interest rates hit banks' profits.
The annual 0.6% charge will take affect from May.
UBS already imposes charges for large accounts held in Swiss francs by companies and some wealthy clients.
Banks' profits have been hit by the European Central Bank's policy of stimulating growth through negative interest rates and increased liquidity.
The ECB penalises banks that store euros with it in an effort to make them lend rather than hoard their cash.
It imposes a so-called negative rate, equivalent to four euros annually on each 1,000 euros that lenders deposit with the central bank.
Banks in Sweden and Switzerland, which are outside the eurozone, pay a similar charge.
A UBS spokesman said: "This charge reflects the increasing costs seen across the industry of reinvesting cash from deposits in money and capital markets, the continued extraordinarily low and negative interest rates in the euro area and increased liquidity regulations."
Commerzbank has even considered storing cash in vaults to avoid paying ECB fees.
The policy of penalising banks has come under criticism in Germany because it discourages saving.