"The report was made by the on-field umpires (Ulhas Gandhe and Chris Gaffaney) according to the IPL's Suspected Illegal Bowling Action Policy," said an IPL statement.
"Mr Narine will be placed on the Warning List and is permitted to continue to bowl in the tournament."
Another report for the 32-year-old Narine will make him ineligible to bowl in the Twenty20 tournament until cleared by the Board of Control for Cricket in India's suspect bowling action committee.
Narine has been reported for chucking several times during his nine-year-old international career and was barred from bowling in 2015 by the International Cricket Council but came back with a re-modelled action.
But his action was once again under scrutiny in the 2018 Pakistan Super League.