The former top-ranked batter played his 58th Test in the World Test Championship final against South Africa in June before Australia dropped him for the subsequent three-Test series in West Indies
Starc was not included in Australia's T20I squad released on Tuesday for the upcoming series against New Zealand.
Cummins has already been rested from a number of white-ball fixtures, including home Twenty20 and One-day International series against South Africa
The 36-year-old, who played 149 ODIs, blasting 3,990 runs, said he was starting to feel the physical toll of the 50-over game
India's board (BCCI) said on Monday the remaining 17 games would resume from May 17 with the final rescheduled for June 3
