Flexcoin, the Canada-based Bitcoin bank, is to close after losing $600,000 in a hacker attack.
Its entire stock of Bitcoins stored on-line, in its so-called "hot wallet", were stolen.
Coins held in "cold storage" or in servers not connected to the internet were not taken.
Last week, the world's biggest Bitcoin exchange, Mt Gox, filed for bankruptcy protection after it suffered a $500m theft.
Bitcoin is a digital or crypto-currency which is bought and sold online, but not backed by any country's central bank or government.
Flexcoin called itself the first Bitcoin bank. It provided centralised storage and enabled instant free transfers between Flexcoin customers.
It said in a statement: "On 2 March 2014, Flexcoin was attacked and robbed of all coins in the hot wallet. The attacker made off with 896 [Bitcoins].
"As Flexcoin does not have the resources, assets, or otherwise to come back from this loss, we are closing our doors immediately.
"Users who put their coins into cold storage will be contacted by Flexcoin and asked to verify their identity. Once identified, cold storage coins will be transferred out free of charge."
Flexcoin and Mt Gox are not the only casualties in Bitcoin's battle with security. On Tuesday, Poloniex, another exchange, also admitted that 12.3% of its reserves had been stolen by hackers.
The Slovenia-based Bitstamp had to halt business temporarily after a cyber-attack in February.
The payment processor Inputs.io was hacked in October to the tune of $1m.
The Bitcoin market has shrugged off the latest thefts. Since the beginning of March, the value of a Bitcoin has risen from $561 to $668.
There are plans by several governments to regulate Bitcoins. A Japanese government spokesman said talks on Bitcoin guidelines were in progress.
The Nikkei Business Daily reported on Wednesday that the government would tax Bitcoin transactions and ban banks and securities firms from handling the digital currency.
US Federal Reserve Chair Janet Yellen said last week the US Congress should look into legal options for regulating virtual currencies such as Bitcoin.
But in the UK, tax authorities published a briefing on the taxing of Bitcoins, dropping plans to charge value added tax (VAT), or sales tax, on Bitcoin trading.