The regulator has assured the company's 10,000 domestic customers their energy supply will continue as normal and outstanding credit balances will be protected.
Ofgem said it would choose a new supplier to take on Future Energy's customers, who will be contacted individually when the process is complete.
It advised Future Energy customers against switching supplier, but to take a meter reading and wait until the new supplier makes contact.
Rob Salter-Church, Ofgem's interim senior partner for consumers and competition, said: "If you are a customer of Future Energy there is no need to worry as we will make sure your energy supplies are secure and your credit balance is protected.
"Ofgem is working to choose a new supplier as quickly as possible for you. Whilst we're doing this, our advice is to sit tight and don't switch. You can continue to rely on your energy supply as normal - in fact the only thing that will change is that you'll get a new supplier."
Citizens Advice director of energy Victoria MacGregor said: "Future Energy customers' gas and electricity will continue as normal - so they'll still be able to heat and light their homes.
"It's important these customers sit tight and wait for Ofgem to organise the new supplier. Switching to another energy company at this stage could mean they don't get any refunds they may be entitled to.
"In the meantime, customers will need to take a reading of their gas and electricity meters for their new supplier."