Cummins flew back home after the second Test in Delhi to be with his mother, and Smith led the side to victory in Indore.
Cricket.com.au reported that Cummins will remain in Sydney.
Three ODIs follow the final Test and a decision on Cummins’s participation in those games will be taken later.
Smith had captained Australia to a nine-wicket win in Indore last week. India lead the series 2-1 and need a win to qualify for the World Test Championship (WTC) final.
With the victory in Indore, Australia secured their qualification for the WTC summit clash in London in June.
According to cricket.com.au, Nathan Ellis has been brought in to replace the injured Jhye Richardson in Australia’s ODI squad.
The ODI series begins March 17.
(With agency inputs)