The 30-year-old vice-captain doubled over in pain after pulling off a sensational catch to remove Alex Carey in the third ODI in Sydney on Saturday.
He was rushed to hospital with the Board of Control for Cricket in India revealing he suffered internal bleeding.
"I'm currently in recovery process and getting better every passing day," Iyer said on social media in his first comments since the incident.
"I'm deeply grateful to see all the kind wishes and support I've received -- it truly means a lot to me.
"Thank you for keeping me in your thoughts," he added.
India's Twenty20 captain Suryakumar Yadav on Tuesday said doctors and physiotherapists described the injury as "rare".
"But rare things happen to rare talent. God is with him and he will recover soon and we will take him along with us," he said.
Iyer is not part of India's T20 squad, which will play the second of five matches against Australia at a sold-out Melbourne Cricket Ground on Friday.
The opening game in Canberra was washed out.