It is a minor setback for the team and Pandya, who returned to action during the limited-overs series in New Zealand after being handed a provisional suspension for his loose talk on women on a TV show.
The BCCI also lifted the interim suspension on batsman K L Rahul, who was on the same chat show.
"The BCCI Medical team decided to rest the all-rounder and let him undergo strength and conditioning work for his lower back at the National Cricket Academy (NCA) in Bengaluru. Mr. Pandya will begin his strength work from next week," said the BCCI in a statement.
"The T20I squad will now consist of 14 members. Mr. Ravindra Jadeja has been named the replacement for Hardik Pandya for the 5 ODIs," it added.
Both Pandya and Rahul still face an inquiry for their controversial comments.
While an out-of-form Rahul was sent back to play at the India A level, Pandya made an instant impact in his comeback game, proving how crucial his presence is for the balance of the side.
The 25-year-old has so far played 11 Tests, 45 ODIs and 38 T20s.
His absence from the ODI squad gives Jadeja another opportunity to stake his claim in the squad for the World Cup to be played in the UK in May-July.
India will host Australia for two T20s and five ODIs, starting Saturday in Visakhapatnam. The second T20 will be played in Bengaluru on February 27.
The five ODIs will be staged in Hyderabad (March 2), Nagpur (March 5), Ranchi (March 8), Mohali (March 10) and Delhi (March 13).