"We can not lift the restrictions without reassuring ourselves that the firm has been able to satisfy all our concerns for example that all clients' money is safe".
The freeze follows the collapse of Wirecard's German parent company on Thursday, following an accounting scandal.
Some have spoken of their frustration, but their money should be safe.
That in turn forced firms that had been relying on Wirecard services to temporarily suspend their own, leading scores of customers to complain on social media about losing access to vital services - and money.
Wirecard UK will be allowed to process fund withdrawals from its users, merchants and clients on the behest of their instructions, with transactions overseen by the FCA.
"We are continuing to do this and on 26 June, we took additional measures to require the firm to cease all regulated activities in order to further protect customer money". These include the likes of Revolut, Pockit, Soldo, Anna Money, and Curve.
It said there are around 50,000 cards in circulation but can not confirm the amount of money on them.
The cards can not now be used by customers in Ireland or overseas, until further notice.
It asked customers to carry a backup card.
An Post said its Money Currency cards - marketed as an affordable way for customers to bring and use money overseas - were issued by United Kingdom based Wirecard Card Solutions Limited. "We apologize for any inconvenience this may cause and we'll update you with more information as soon as we have it", the company added.
"WDCS is working hard to have the steps in place which will enable the suspension to be lifted so business can resume as usual. We will provide further updates on our website as soon as we can".
Funds are not protected, as they are in banks, by the Financial Services Compensation Scheme, but the firm said customers' money was held safely in segregated accounts.
The FCA has told people affected to contact their card provider.
Wirecard AG filed for insolvency on Thursday.
The news comes just days after Markus Braun, the ousted Chief Executive of th global payment processing firm, was arrested on charges of corruption, fraud and executive mismanagement. The firm's creditors stand to lose billions of euros from the scandal.
The Munich based firm employs nearly 6,000 staff in 26 countries.