Narine, 27, was reported after the first one-day international against Sri Lanka in Pallekele on Saturday, where he went wicket-less in the 19-run defeat for the West Indies.
Narine’s action had in the past been questioned during domestic competitions like the Indian Premier League, but this was the first time he has been reported in an international match.
An ICC statement said Narine, who pulled out of the World Cup earlier this year to work on his action, will be allowed to play on till the results of the tests are declared.
Narine has played six Tests, 55 one-dayers and 32 Twenty20 internationals since his debut in 2011.
The ICC launched a crackdown against suspect actions in June last year, leading to several leading bowlers being reported.
Other bowlers who have been up hauled up include Pakistan’s Saeed Ajmal and Mohammad Hafeez, Bangladesh’s Sohag Gazi, New Zealand’s Kane Williamson, Sri Lanka’s Sachithra Senanayake and Tharindu Kaushal, and Zimbabwe’s Prosper Utseya and Malcolm Waller.