Australia captain Pat Cummins will remain in Sydney and miss the third Test against India in order to be with his seriously ill mother.

Cummins flew home to Australia on Sunday night, immediately after the team's second Test defeat to India in Delhi, to be around his family.

The 29-year-old on Thursday night informed coach Andrew McDonald of his decision to remain in Australia, with the rest of the squad told at training on Friday morning.

"I have decided against returning to India at this time as my mother is ill and in palliative care. I feel I am best being here with my family," Cummins said in a statement.

"I appreciate the overwhelming support I have received from Cricket Australia and my teammates. Thanks for your understanding."

Cummins intends to be available for the fourth and final Test in Ahmedabad, but it is possible he will sit out the rest of the series.

The star fast bowler was expected to return to India on Friday ahead of the third Test in Indore, starting on March 1.

However, Cummins's family situation will prevent him from making the trip back, with Steve Smith to fill in as captain.

It will be the third time Smith has stepped in as Test captain since Cummins became skipper in November 2021.

Cummins has been forced to sit out the two most recent pink-ball matches in Adelaide against West Indies and England due to injury and COVID-19.

Smith left the Australian camp in Delhi for a brief break to Dubai with wife Dani and arrived back in the Indian capital on Thursday night.

Cummins's absence is another blow for Australia's hopes of winning at least one Test in this series to book its spot in the World Test Championship final.