Attorney General Dominic Grieve has blocked the release saying the letters reflected the Prince of Wales "most deeply held personal view and beliefs".
Last month, a three-judge bench had ruled that the correspondence by Charles, 63, should be published.
But Grieve said it was an exceptional case where the letters formed part of the prince's "preparations for kingship". Publishing the "frank" views would "seriously undermine" his ability to fulfil his duties as King.
"The ability of the Monarch to engage with the government of the day, whatever its political colour, and maintain political neutrality is a cornerstone of the UK's constitutional framework," Grieve was quotes as saying by BBC.
The Administrative Appeals Chamber said last month that in its view, it was in the public interest "for there to be transparency as to how and when Prince Charles seeks to influence government".
The case arose from a Freedom of Information request submitted by a journalist.
Grieve said the letter-writing was part of Charles' preparation to succeed his mother - Queen Elizabeth II - to the throne. Charles is standing next in line since 1952.
