The UAE summoned the Qatari ambassador over what it said were insults against the UAE made by a prominent cleric in a broadcast from Doha, state news agency WAM reported on Sunday.
The diplomatic incident reflects growing splits between the two members of the Western-allied Gulf Cooperation Council in their approach to Islamists emboldened by the 2011 "Arab Spring" protests that forced four heads of state from power.
While Qatar has sided with Islamist groups such as the Muslim Brotherhood, the UAE has taken the opposite tack, cracking down on Islamists at home and supporting Egypt's military-backed administration.
UAE news agency WAM said the foreign ministry had handed the Qatari ambassador "an official protest memorandum over the insolence shown by the so-called Youssef Al Qaradawi towards the United Arab Emirates".
In a sermon two weeks ago delivered at a mosque in the Qatari capital Doha and broadcast by state television, Qaradawi condemned the UAE as a country which was against Islamic rule, UAE media reported.
"We have waited for our neighbour to express a clear rejection of this insolence and to offer sufficient clarifications and assurances for this misrepresentation and incitement against the UAE," WAM quoted UAE Minister of State for Foreign Affairs Anwar Gargash as saying.
"But unfortunately, and despite the self restraint and calm approach, we found no desire or response for such a thing from the brothers in Qatar," he added.
"It is shameful that we allow Al Qaradawi to continue his insults of the UAE and the ties (that bind) the peoples of the Arabian Gulf," Gargash said on Twitter.
UAE media quoted Qatari Foreign Minister Khaled al-Attiyah as saying that Qaradawi's comments did not reflect Qatar's views.
"The foreign policy of Qatar is expressed and conveyed only through the official channels of the state," Attiyah said, according to the English language Gulf News.
A Qaradawi aide told Reuters that the cleric had expressed his own views and that he would not stop, adding that "Qatar allows him to say what he wants as an individual and that no one had called him over the remarks".