"Phil's absence will not affect the release of our new album Rock or Bust and upcoming tour next year," the statement added.
Rock or Bust is due to drop Dec. 2 in the U.S.
Rudd, who has been nicknamed the "Hugh Hefner of Tauranga" by local press, was granted bail at a court appearance in Tauranga, New Zealand, after being arrested Thursday morning on charges of attempting to procure the murders of two people.
The 60-year-old was also charged with possession of methamphetamine, possession of cannabis and threatening to kill. The maximum penalty for procuring a murder is 10 years in jail, while threatening to kill carries a maximum of seven years.
He entered no plea to the charges and will next appear in court on Nov. 27.
Former manager Michael Browning, who recently released Dog Eat Dog, a memoir of his time with the band, told Fairfax Radio in Brisbane that Rudd was a "fabulous drummer" and "universally recognized as a crucial part of AC/DC."
He said the departure of founding member Malcolm Young, who is suffering from dementia, plus Rudd's possible future absence would challenge the band, although a replacement drummer could easily be found for their upcoming tour, according to New Zealand's Stuff.
"I guess where it really becomes a problem is future recordings. When you don't have Malcolm and Phil Rudd, you lose a lot of the essence on the creative level in the recording studio and I really can't envisage that continuing," he told Fairfax Radio 4BC.
"Who knows? They're good at overcoming adversity, AC/DC."