Prosecutors said the 61-year-old Australian rocker phoned a former employee last year and said, "I'm going to come over and kill you."
Police found methamphetamine and cannabis during a search of Rudd's New Zealand home in November.
Rudd, who played with AC/DC for a total of 30 years, initially denied the allegations against him, but made a surprise guilty plea in April.
Under his sentence, he will be electronically monitored for eight months and will also have to complete a rehabilitation program, CNN affiliate TVNZ reported
Judge Thomas Ingram told Rudd that there "was nowhere to hide" and that he would face jail if he was found to have any traces of drugs or alcohol in his system, according to the broadcaster. The maximum sentence in New Zealand for threatening to kill is seven years in prison.
Ingram said Rudd had clearly been unable to deal with a long-running meth addiction, according to TVNZ. The judge was unmoved by the drummer's argument that the convictions would hurt his chances of playing with AC/DC again.
"Queen replaced Freddie Mercury, and your band is touring without you now," Ingram said.
Rudd's lawyer, Craig Tuck, told CNN that he had filed an appeal against the sentence Thursday and was still seeking to have his client discharged without conviction.
Threat after solo album flopped
According to a court summary from April, Rudd fired several of his employees last year because his solo album, "Head Job," had flopped in the charts after its release in August.
Prosecutors say he called an associate in September and said he wanted his former personal assistant "taken out." Rudd later phoned the former personal assistant and made the threat to kill him.
Tuck has described the matter as "essentially just an angry phone call."
Rudd is not currently a member of AC/DC
, whose world tour this year will include shows in New Zealand in December.
When charges were first filed against Rudd in November, interest in his case reportedly prompted a bump in sales
for "Dirty Deeds Done Dirt Cheap," the band's classic song about a hit man vaunting his services.
An earlier police charge against Rudd of attempting to procure murder was dropped in November after prosecutors decided there wasn't enough evidence.