The 32-year-old was reported after helping his domestic Lions side into the final of South Africa's provincial 50-over competition on Wednesday when he took 2-38 in eight overs.
"Phangiso's action will now be scrutinised further in accordance with the CSA regulations," governing body Cricket South Africa said in a statement on Thursday.
"He is required to undergo independent analysis by a member of the ICC panel of human movement specialists and is permitted to continue bowling until the results of the testing are known."
The spinner will require to undergo testing within 14 days and will hope to be cleared before the March 8-April 3 World Twenty20. South Africa open their campaign at the biennial event on March 18 against England in Mumbai.
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It is the latest setback for Phangiso, who was disciplined by CSA late last year after allegedly offending crew and passengers on a flight from India while in an intoxicated state.
He was also forced to apologise after being caught by television cameras imitating snorting cocaine while in his team's dugout during the second Twenty20 international against England at The Wanderers on Sunday.
Phangiso has played 16 one-day internationals and nine T20 internationals for South Africa.
(Reporting by Nick Said; editing by Sudipto Ganguly)
