The Zimbabwe Cricket Union's (ZCU) decision, accepted by the Australians, came just hours before an International Cricket Council (ICC) teleconference which was likely to strip the series of its Test status.
Zimbabwe were to field a weakened team after 15 white rebel players walked out over a dispute over selection.
"The Zimbabwe Cricket Union and Cricket Australia have agreed to adjourn the Test matches to a date to be fixed and have requested the ICC executive board to endorse this agreement at its June meeting," a statement read out a news conference by Cricket Australia chairman Bob Merriman.
"We are saying we should not be playing the Test matches in the interests of Test match standards throughout the world."
Three one-day matches will go ahead, he said.
