Cricket Australia has confirmed the left-arm spinner's action was reported after the second Test in Sri Lanka.
He must now go for biomechanical testing, with the results to be referred to the International Cricket Council.
Kuhnemann potentially faces a ban if the ICC rules his action is illegal.
Kuhnemann was a breakout star in Sri Lanka, leading the Australian bowling with 16 wickets at an average of 17.18 as Steve Smith's men swept the two-Test series.
He has received strong support from CA.
"The Australian team was notified of the match officials' referral following the second Test against Sri Lanka in Galle and will support Matt through the process of clearing this matter," a CA spokesperson said.
"Matt has played 124 professional matches since his debut in 2017, including five Test matches and four one-day internationals.
"He has played 55 Big Bash League games since 2018. This is the first time in those eight years of professional cricket that his action been questioned.
"Cricket Australia will liaise closely with the ICC and independent experts in line with ICC regulations. No further comment will be made by Cricket Australia or Matthew until the matter is resolved."
Kuhnemann, who plays domestically for Tasmania and the Brisbane Heat, is not in the Australian squad for two one-game internationals in Sri Lanka.
He will reportedly undergo testing in Brisbane over the next few weeks.
AAP understands Kuhnemann's action has been tested previously and was found to be in the legal range.
Under cricket rules, a player is allowed 15 degrees of flex in their bowling arm.
Kuhnemann recovered from a significant thumb injury to star in Sri Lanka as Australia won a Test series there for the first time in 14 years.
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