The "hitman" charge was laid by police without consulting the crown solicitor, Mabey said.
"The charge alleging an Attempt to Procure Murder should never have been laid. The Crown Solicitor's opinion was not sought. The charge is now withdrawn -- within 24 hours of Mr Rudd's first appearance in Court," Mabey said in a statement.
The other charges of threatening to kill and possession of methamphetamines and cannabis remain. Rudd will defend the charge of threatening to kill, Mabey said, adding that the drug possession charges are minor.
Rudd was arrested at his home in Tauranga, New Zealand, on Thursday morning and received bail following a court appearance on Thursday afternoon local time.
In the statement, Mabey said Rudd had suffered "incalculable" damage to his reputation.
"Mr. Rudd has suffered unnecessary and extremely damaging publicity as a result of widespread and sensational reporting of a very serious allegation, which on any basis was never justified."
He added that Rudd is considering any possible remedies he may have.
Rudd remains out on bail until his next court appearance on Nov. 27.
AC/DC said in a statement Friday, following Rudd's arrest, that "Phil's absence will not affect the release of our new album Rock or Bust and upcoming tour next year."