Bumrah, who remained the most successful bowler in the recent Border-Gavaskar Trophy, picked up 21 wickets at an average of 17 and strike-rate of 44.9.
"Keeping in mind the workload of the bowler (Bumrah), it was best felt to give him adequate rest ahead of the home series against Australia," a BCCI statement said on Tuesday.
Bumrah has been replaced by Mohammed Siraj, who has played three T20I so far since his international bow against New Zealand last year. Siraj has also enjoyed a good run with India A in New Zealand, taking seven wickets in three first-class games.
The selectors have also called up Siddarth Kaul, who has proved himself against New Zealand A for the three-match T20I series. He finished with seven wickets from three List A games, with a best of 4/37.
"Mohammed Siraj will replace Bumrah in the squad for the Australia and New Zealand tour. Siddarth Kaul has also been drafted into the squad for the 3-match T20I series against New Zealand," the statement added.
India and Australia are slated to play a three-match ODI series from January 12 to 18. The Men in Blue will then tour to New Zealand to play five-match ODI series and three-match T20Is, starting from January 23.
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