I am really sad that I won't be able to participate in Melbourne, especially after winning the last Grand Slam in New York," said Cilic, who beat Kei Nishikori to win his first Grand Slam title last September.
"But I was advised by doctors to be careful as much as possible to avoid even more serious problems.
"It is improving day by day, but I still don't feel fit enough to be able to compete at the highest level.