The part-time spinner's action raised concerns among the match officials about its legality after the match in Sydney.
Rahul and Pandya were axed ahead of India's opening ODI against Australia in Sydney on Saturday
The Australians made 288 for five off their 50 overs after winning the toss and restricted India to 254 for nine.
The announcement comes hours before the start of the first one-day international of a three-match series against Australia starting Saturday in Sydney
"It's just an opportunity to see Alex play in a position he's done quite bit of now in Big Bash and one-day cricket," said fellow opener Finch
It is another blow for Marsh who was axed from the Test squad to play Sri Lanka, along with his brother Shaun.
The BCCI gives bonuses for major tournaments like the World Cup or Champions Trophy but extra payments for a bilateral series is rare.
"Keeping in mind the workload of the bowler, it was best felt to give him adequate rest ahead of the home series against Australia."
Sikandar Raza notches up Euro T20 Slam deal
Multan Sultans pacer to feature in Euro T20 Slam
Babar Azam joins Somerset for Vitality Blast
Most successful bowler in the history of PSL
Shadab vows to contribute more in upcoming matches
Dharmasena admits his 'error of judgment' in World Cup final
'To us, it feels like it's shrinking' – Sikandar Raza hints at ICC's failure to 'grow the game'
Dean Jones tears up while defending Asif Ali
Shane Watson continues his prime form in PSL
Lendl Simmons and Tymal Mills join Peshawar Zalmi