Iyer, 30, sustained an impact injury in his left lower rib cage region as he pulled off a sensational backpedalling catch to remove Alex Carey, a key moment in the third one-day international that India won by nine wickets.
Despite the victory, India lost the series 1-2 after suffering defeats in the first two games in Perth and Adelaide.
Iyer, who is also the vice-captain of the ODI team, was forced off the field after the injury and did not return for the rest of Australia's innings.
"He was taken to the hospital for further evaluation," the Board of Control for Cricket in India (BCCI) said in a statement.
"Scans have revealed a laceration injury to the spleen. He is under treatment, medically stable, and recovering well."
He remains hospitalised in Sydney where the BCCI medical team is closely monitoring him in consultation with specialists from Australia and India, the statement added.
It was not clear when Iyer could return to action.
A five-match T20 series between the two cricketing powerhouses begins on October 29 but Iyer is not a part of that squad.
India's next one-day outing is a home series against South Africa, starting November 30.
Iyer has scored 2,917 runs from 73 ODIs at an average of 47.81.
