Rhodes, who is the fielding coach of IPL's Mumbai Indians team, was in Hyderabad for the league's final match yesterday when his son was born.
Rhodes' wife gave birth to the baby, weighing around 3.7 kg, last evening without any complication through water delivery, Dr Amit Dhurandar of Surya Hospital in suburban Santacruz told PTI.
Both the mother and the newborn are doing fine, he said, adding that they may be discharged by tomorrow.
Mumbai Indians won the Indian Premier League's final in Hyderabad last night.
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Rhodes' daughter, named India, was also born at a hospital in the city two years ago during the IPL 8 season.
Dr Dhurandar said, "Rhodes wanted the baby's delivery through water birth and he wrote to me a few months back.
"Since water birth isn't easily available in South Africa, therefore, they opted this mode of delivery here in the Mumbai city, which is becoming popular among the Indians too," he said.