Sheikh Abdullah bin Ali Al-Thani, a little-known royal, emerged as a key figure in the dispute between the Gulf states in the weeks after Riyadh and Abu Dhabi cut ties with Doha in June.
He is seen by some as a potential challenger to the Qatari leadership.
A video circulating online, also broadcast by Qatar-based Al-Jazeera television, shows the sheikh warning that he was "afraid something could happen to me that will be blamed on Qatar".
"I am now in Abu Dhabi, where I was a guest of (UAE crown prince) Sheikh Mohammed" bin Zayed al-Nahyan, said Sheikh Abdullah.
"That is no longer the case. I am now detained."
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"I want to make clear that the people of Qatar are innocent," the sheikh said. "Sheikh Mohammed bears full responsibility for anything that happens to me."
The UAE denied that Sheikh Abdullah was being held against his will, with state news agency WAM reporting he was in the country "at his own behest".
"Sheikh Abdullah has had unrestrained mobility and freedom of movement during his stay in the UAE," WAM cited an unnamed foreign ministry official as saying.
"Subsequently Sheikh Abdullah had expressed his desire to leave the UAE following which all measures were taken to honour his desire without any reservation."
Ali Rashed al-Nuaimi, who heads the UAE's Hedayda counter-extremism centre, meanwhile tweeted that Sheikh Abdullah had asked to stay in the Emirates "for his own safety".
"For the record, a trusted source confirmed that Sheikh Abdullah bin Ali Al-Thani is free to leave the United Arab Emirates as he likes and to whatever destination he likes," Nuaimi wrote.
Saudi Arabia, the UAE, Egypt and Bahrain severed diplomatic and trade ties with Qatar in June over allegations that Doha supported Islamist extremists and had close ties to regional rival Iran. Doha denies the accusations.
In response to the video, Qatar's foreign ministry spokesperson, Lulwa al-Khater, said Doha was monitoring the situation.
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"The state of Qatar observes the situation closely, and due to the total severance of ties with the UAE it is difficult to clearly establish the circumstances surrounding the situation," she said in a statement.
"Despite that, the State of Qatar principally stands with the protection of rights for every individual and affirms the entitlement of his family to pursue all legal means for the protection of his rights."
In August, Sheikh Abdullah met powerful Saudi Crown Prince Mohammed bin Salman to mediate on reopening a land border to allow Qatari pilgrims to perform the annual Muslim pilgrimage to Mecca.
It was the first public high-level encounter between the two nations since the diplomatic crisis erupted.
Doha was quick to point out that he was in Saudi Arabia in a personal capacity and did not represent the government.
Qatari officials also accused Gulf rivals of seeking regime change in Doha and replacing Emir Sheikh Tamim bin Hamad Al-Thani with Sheikh Abdullah -- who belongs to a branch of the Al-Thani family that has seen its power eroded but is still well-connected in the Gulf.
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