The current deal expires at the end of April and does not affect the remainder of this summer's broadcast schedule on Radio Sport.
Radio Sport has been broadcasting cricket for more than 20 years and New Zealand Cricket will now go to the market to see what other interest there is picking up the broadcast rights.
RNZ understands NZME had been seeking a five year deal but New Zealand Cricket felt given the changing media landscape that period was too long.
In a tweet, Radio Sport said: "NZME has chosen not to renew the rights to broadcast live commentary of New Zealand Cricket's home internationals plus domestic games from next summer. Radio Sport still holds rights until the end of this summer."
In a subsequent tweet it said: "After lengthy discussions with New Zealand Cricket, we haven't been able to reach agreement."
Subsequently, NZME's Managing Editor Shayne Currie tweeted that it was "sad it's come to this - speaking as a huge cricket lover as well."
The New Zealand Herald quoted NZME's Head of Talk Jason Winstanley as saying the move opened the way for Radio Sport to change its schedule to appeal to a wider audience.
He said: "We have been in discussions with New Zealand Cricket for some time but haven't been able to reach agreement on the rights. Our cricket coverage has run at a loss - something we've previously been prepared to wear, but we're now taking the opportunity to rethink our offering in this space."