The incentive package was only launched in early June but has already gone through its £120 million budget due to “overwhelming demand”.
A spokesperson for Decc told Utility Week that no decision has been made as to whether the GDHIF will be re-introduced.
The incentive scheme offered householders up to £7,600 to make their propriety more energy efficient.
All applications received prior to the fund closing that satisfy the terms and conditions and meet the eligibility criteria will be honoured at the original rates.
Amber Rudd, parliamentary under secretary of state for energy and climate change, said: “The GDHIF is a world first and in a short space of time it has proved extremely popular.
“We were always clear there was a budget which is why we encouraged people to act quickly.
“As a result, thousands more families will now benefit from Government help to have warmer homes which use less energy.”
Shadow climate change minister Jonathan Reynolds said: “This is a shocking act of incompetence by Government Ministers.
“A fund that was supposed to last the year, and compensate for the cuts to energy efficiency measures announced last December, has run out after just six weeks.”
He called for the Public Accounts Committee to investigate the issue and for the government to provide “clear answers on how they will resolve the mess they have created”.
The Green Deal was created to work alongside the energy company obligation (Eco), to not only help improve the energy efficiency of the UK housing stock, reducing energy demand and energy bills, but also to help keep the costs for the suppliers of installing energy efficiency measures under Eco low.
Richard Twinn, policy and public affairs officer at the UK Green Building Council, said: “The sudden and immediate closure of this fund is another setback for the energy efficiency industry because companies have specifically geared up to market and deliver through this scheme.
“These constant changes are not helpful to industry. We now need urgent clarity as to whether Government will bring forward any more money to ensure continuity of Green Deal work.
“This does demonstrate that we need long-term drivers, not short term pots of cash to avoid this continual cycle of boom and bust.”