Greinke's schedule has been thrown off by a strained right calf, and he won't be ready to throw the planned 90 pitches in a game by March 22, when the Dodgers open a two-game series Down Under.
"From a standpoint of having 90 pitches, he won't be there," Mattingly said, according to MLB.com.
Greinke reported some improvement Monday but has no set schedule for a return to the mound, according to the website.
Greinke, the Dodgers' No. 2 starter, was hurt Thursday while throwing only four pitches in a spring training outing against Arizona. He has undergone treatment and played catch but was scratched from his scheduled start Tuesday against the Seattle Mariners as the team remains cautious with his rehabilitation.
Reliever Brian Wilson will take his place against Seattle.
Greinke sparked some controversy earlier this spring by saying he had "zero excitement" for pitching in Australia, then clarified his remarks to say he had nothing against the country but was not a fan of disrupting his routine.
Also Monday, right-hander Ross Stripling, a top prospect, left the Dodgers to return to Los Angeles for an MRI on his right elbow. He has thrown two innings in spring training games but might need major surgery for ligament damage.
The Associated Press contributed to this report.