The scheme was introduced by the Irish government four years ago to forge connections with some of the 70m people abroad who claim to have Irish roots.
It was an official confirmation of Irish ancestry, aimed at those who do not qualify for full citizenship.
However, as few as 3,000 certificates have been sold since the 2011 launch.
In a statement, the Department of Foreign Affairs said: "The uptake of the Certificate of Irish Heritage has been considerably less than anticipated.
"No further certificates will be available for purchase after 24 August 2015."
The department said the scheme had been set up to encourage people of Irish descent to trace their family roots and to give "greater practical expression to the sense of Irish identity felt by many around the world".
Previous recipients have included a number of high-profile figures, including US President Barack Obama, former US President Bill Clinton and the Hollywood actor Tom Cruise.
Applicants were asked to provide details of their Irish ancestors online, so their ancestry could be verified through record checks.
The certificates cost 45 euros (Â£32) or 120 euros (Â£85) for a framed version, but the Department of Foreign Affairs said it never anticipated that the scheme "would provide significant revenue to the government".
The website where applications are processed described the initiative as representing the "enduring emotional ties and sense of identity bestowed by Irish ancestry, recognising the continuing emotional attachment of the descendants who left our shores long ago".

Head coach Warren Gatland is leading the British and Irish Lions in New Zealand and has named interim coach Rob Howley as part of his backroom team.
Forwards coach McBryde assumes head coach responsibilities for the third time after leading Wales on tours in 2009 and 2013.
"It is an honour to represent your country and to do so overseas carries extra responsibility," said McBryde.
"For me it is another exciting opportunity to lead the team.  It is something I have thoroughly enjoyed in the past and I'm really looking forward to doing it again at the end of the season."
The Welsh Rugby Union (WRU) will appoint assistant coaches for the summer tour to assist McBryde.
"We are also at an advanced stage in discussions with a number of other individuals about the summer tour and hope to be in a position to confirm the full make-up of the management team next week," said WRU chief executive Martyn Phillips.
Union chairman Gareth Davies, who is also on the Lions' selection panel, believes the involvement of Welsh coaches will benefit the national team.
"2017 is a real summer of opportunity for Welsh coaches and should benefit the whole of Welsh rugby in the years ahead," he said.
"It is not often that you get the opportunity to develop coaches in different environments.
"Our coaches and players have been invigorated by their Lions experiences on previous campaigns and there is little doubt that a tour of New Zealand will provide the ultimate test and so once again both mentally stimulate and inspire each individual."

2 January 2017 Last updated at 07:05 GMT
Now it's 2017 is and there's plenty going on to look forward to!
So to get you ready we here at Newsround have put together a video with loads of stuff for you to look out for.
Have a watch, it's full of dates to remember!

She was artificially inseminated earlier this year after attempts to bring her together with male partner, Yang Guang, failed.
The zoo said new scientific tests had given a "strong indication" of pregnancy, but were "too new to be definitive".
Tian Tian also conceived last year, but the pregnancy failed.
Iain Valentine, director of Giant Pandas for the Royal Zoological Society of Scotland, said: "The latest scientific data suggests Tian Tian the giant panda is now pregnant and that implantation has taken place, therefore she may give birth at the end of the month.
"This is all very new and complex science and we still have a bit of time to go yet.
"As like last year, the late loss of a cub remains entirely possible."
The zoo said it had been able to confirm that Tian Tian did become pregnant last year.
However, it said it was most likely that she had reabsorbed the foetus late term.
The two pandas arrived in Scotland from China in 2011.
Tian Tian has had cubs in the past in China, before she came on loan to Edinburgh.
If she does have a successful delivery, it will be the first time a giant panda has been born in Britain.
The panda enclosure at Edinburgh Zoo is due to close to visitors from Saturday ahead of a possible birth.
The Certificate of Irish Heritage scheme, which officially recognises people of Irish descent around the world, is to end due to a low uptake.
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Robin McBryde will coach Wales on their summer tour of the Pacific Islands.
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2016 has come to an end and it certainly was an eventful year.
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Edinburgh Zoo has said it believes its panda Tian Tian is pregnant and may give birth at the end of the month.