The left-armer injured his right little finger while fielding in the five-wicket loss in Indore on Sunday, team doctor Richard Saw said in a statement.
"Following the conclusion of the match he went for X-rays which have confirmed a fracture of the finger," Saw said.
"He will return home to Australia and consult a specialist with a possibility of surgery."
Agar will not be replaced in the squad for the remaining two ODI matches, CA added.
Injuries have already ruled pace bowlers Mitchell Starc, Josh Hazlewood and James Pattinson out of the tour.
India took an unassailable 3-0 lead in the five-match series. The fourth ODI is in Bengaluru on Thursday.
(Reporting by Ian Ransom; Editing by Sudipto Ganguly)
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