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".
The Certificate of Irish Heritage scheme, which officially recognises people of Irish descent around the world, is to end due to a low uptake.