RNZ pulled out of the awards from 2010 to 2012, claiming it had become too costly to take part because of a government freeze on its funding.
Thompson insisted the new withdrawal was not about cost cutting.
At the last awards, broadcasters were able to enter without an official representative.
Saturday morning host Kim Hill won awards in 2011 and 2013, according to the Radio Broadcasters Association, which organises the awards.
RNZ officially returned to the awards in 2013, and Hill was recognised for her outstanding contribution to radio.
The awards have centred on the commercial sector - effectively divided between MediaWorks and NZME. - but some categories such as best radio drama and best recorded live event were dominated by RNZ.
Those categories will be withdrawn from the awards next year.
The withdrawal means hosts Guyon Espiner and Susie Ferguson will never be finalists against Newstalk ZB's Mike Hosking and Radio Live's new breakfast host Paul Henry.
Thompson said there were better ways of using the considerable resources required to recognise staff.
He said there were no plans to develop new internal awards.
Radio Broadcasters Association chief executive Bill Francis, who organised the awards, said there were large numbers of entries from RNZ broadcasters for the awards this year.
It was disappointingly to see them go, but the absence of RNZ would not detract from the value of the awards, and they would continue to recognise community access and iwi radio stations.
State broadcaster TVNZ pulled out of the television awards in 2013, arguing there was too little competition to justify the costs of taking part.
The Canon Media Awards, aimed at the print media sector, struck controversy this year when it sought to expand its awards to include best blog.
The award went to Whale Oil blogger Cameron Slater, who was heavily implicated in the Dirty Politics scandal.