Mohammed Siraj the Hyderabad-based fast bowler has been called in as Bumrah's replacement. It was deemed fit to give him adequate rest ahead of the home series against Australia with the upcoming ODI World Cup in England set to be conducted soon as well.
Rohit Sharma will return for the ODI series after skipping the fourth test against Australia to spend time in India with his family.
The Board of Control for Cricket in India released a statement Tuesday saying Bumrah, who bowled more overs than any other pace bowler in the four-test series against Australia, deserved a break.
The decision to rest him comes after captain Virat Kohli also emphasised on managing the workload of the pacers following India's maiden Test series win in Australia here on Monday.
Selectors will also have to ponder whether Nathan Lyon, another player back in the mix, is the right fit in an Australian XI that will be desperate to start the series well after a horror 2018.
Kaul too has been in good form with the ball and recently took 10 wickets in his last two first-class games.
India are slated to play their first ODI against Australia on January 12 in Sydney, followed by the second ODI on January 15 in Adelaide and the third ODI being on January 18 in Melbourne. They will then play three T20Is in New Zealand in February.