Rayudu, 29, scored an unbeaten 124 in the first one-day international against Zimbabwe and followed it up with a 41 in the second match, during which he sustained the injury.
"Rayudu pulled his right quadriceps muscles and will require 2-3 weeks of rehabilitation," the BCCI said in a statement.
Uncapped Sanju Samson, 20, will replace Rayudu for the third and final ODI and the two subsequent Twenty20 matches.
India are 2-0 ahead in the three-match series, with the final ODI on Tuesday.
(Reporting by Sudipto Ganguly; editing by Amlan Chakraborty)
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