Las Hawta, 17, and Rinas Fadhil Ali were both arrested on Wednesday evening, said a source in the prosecutor's office in the regional capital Arbil.
Their Instagram accounts, @las_hawta and @roy_makeup, which also show images of their clients, boast tens of thousands of followers.
Police acted after "indecent images" were posted by the pair "who dress as women", and a "medical report established they are men", the prosecution source said.
Iraq's autonomous Kurdish region likes to present itself as a haven of tolerance but, like the rest of the country, it remains dominated by conservative values.
"The detention of Las and Roy was ordered by the prosecutor general of Iraqi Kurdistan," justice ministry spokeswoman Nariman Taleb told AFP, without elaborating.
In recent weeks, video had circulated on social media of the pair attending a media launch party in Arbil in women's clothing.
Lawyer Aso Hashem claimed that prosecutors had acted after he announced on social media that he planned to lodge a complaint.
He told AFP "the transformation of some men into women... runs against our customs and traditions, Islamic law and Iraqi law."
Wednesday's arrests come amid a spike in anti-LGBTQ rhetoric across Iraq in recent months.
In August, the federal parliament in Baghdad began debating a bill which would allow same-sex relations to be punishable by death in some cases.
At the start of the year, the federal authorities launched a campaign against "indecent content" on social media that saw several YouTubers and TikTokers arrested.
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