Maplin has also collapsed. Almost 6,000 jobs at risk.
Retailer Toys R Us UK has fallen into administration putting 3,200 jobs at risk.
Electricals retailer Maplin has also collapsed into administration, putting 2,500 jobs at risk.
Toys R Us was looking to Europe for buyers to rescue it over the weekend, but it appears no deal could be secured.
The company will continue to trade for now.
Both companies have stores in Swansea and Cardiff.
Chains are juggling a swarm of pressures including rising costs, online competition and dwindling consumer spending.
Moorfields has been appointed administrator to Toys R Us UK, the country's largest toy retailer, which is continuing to trade from each of its 105 stores - at least for now.
It said it would continue to accept gift cards already bought and announced that most remaining stock would be on promotion to assist clearance.
Moorfields partner, Simon Thomas, said: "We will be conducting an orderly wind-down of the store portfolio over the coming weeks.
"All stores remain open until further notice and stock will be subject to clearance and special promotions.
"We're encouraging customers to redeem their gift cards and vouchers as soon as possible.
"We will make every effort to secure a buyer for all or part of the business."
He added: "Whilst this process is likely to affect many Toys R Us staff, whether some or all of the stores will close remains to be decided.
"We have informed employees about the process this morning and will continue to keep them updated on developments.
"We are grateful for the commitment and hard work of employees as the business continues to trade."
It is understood the demise of the UK business will leave the Pension Protection Fund (PPF) - the country's pension lifeboat - facing a bill of about £37m as it absorbs the company's pensions liabilities.
The PPF, like other creditors, had supported a rescue plan before Christmas that had aimed to keep the retailer trading by allowing it to slash some rent bills and trim store numbers.
Toys R Us is struggling internationally, except in Asia. It sought bankruptcy protection in the US and Canada last year.
The chain has previously admitted its 1980s-style warehouse stores had become tired, expensive and suffered particularly from online competition.
Alex Neill from the consumer group Which? said: "It's a worrying time for everyone when a company goes into administration but for customers it's important to remember that your consumer rights may be affected.
"If you have recently bought anything from Toys R Us, you may not be able to claim a refund or exchange the item if they cease trading.
"If you have Toys R Us gift vouchers you should try to spend these in-store as soon as possible.
"If you are planning to shop in Toys R Us and intend to buy something worth more than £100, make sure you use a credit card as you'll be able to make a claim against your credit card company under Section 75 Consumer Credit Act if anything goes wrong," he advised.