The U-turn by authorities, announced less than 24 hours after Phil Rudd appeared in court, was because of a lack of evidence, his lawyer Paul Mabey said.
He will still face charges of drugs possession and making threats to kill.
AC/DC had earlier issued a statement saying its planned tour would not be affected by news of the charges.
The band is one of the highest grossing music acts of all time.
On November 6, Phil Rudd appeared in court after a police raid on his waterfront house in Tauranga, on New Zealand’s North Island.
However, on November 7, prosecuting lawyer Greg Hollister-Jones said his office had reviewed the case and found there was “insufficient evidence to proceed with the charge of attempting to procure murder”.
Phil Rudd’s lawyer, Paul Mabey, said the “charge alleging an attempt to procure murder should never have been laid”.
He added that Phil Rudd had suffered “incalculable” damage from the publicity surrounding the allegation and its sensational reporting, and would consider “any possible remedies he may have”.
He described the drug charges as “minor” offences and said the musician would defend the charge of making threats to kill, which carries a maximum sentence of seven years in jail.
Phil Rudd, 60, is next due in court on November 27. AC/DC is launching its new album on December 2.
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