A BCCI media release confirmed that Rayudu, 29, sustained the injury during the second ODI in Harare and will "require two to three weeks of rehabilitation". Rayudu is the second player to pull out of the squad after a fractured finger ended Karn Sharma's series last week.
Rayudu, who scored a match-winning 124 not out in the first ODI, is currently the leading run-scorer in the series. His withdrawal will give 20-year-old Sanju Samson, who has already played 137 senior matches, a chance to make his international debut.
"The Indian team is the world's best team," Samson said. "I am very lucky to get a call to play for the country"
India secured the one-day series with a 62-run win in the second ODI, and will play the last match in Harare on Tuesday.The two T20 matches are scheduled to be held on July 17 and 19.