The closure of the broadcaster is one of 13 wide-ranging demands placed on Doha by Saudi Arabia and its allies as the price for lifting an almost month-long "blockade" on Qatar.
The four countries have given Qatar a 10-day deadline for implementation ending on July 4.
UN rights chief Zeid Ra'ad Al Hussein "is extremely concerned by the demand that Qatar close down the Al Jazeera network, as well as other affiliated media outlets," his spokesman Rupert Colville told reporters.
"The demand that they be summarily closed down is, in our view, an unacceptable attack on the right to freedom of expression and opinion."
Colville stressed that countries that take issue with items broadcast on other countries' television channels, "are at liberty to publicly debate and dispute them."
"To insist that such channels be shut down is extraordinary, unprecedented and clearly unreasonable," he said.
He warned that if Qatar goes ahead and shutters Al- Jazeera, "it would open a Pandora's Box of powerful individual states or groups of states seriously undermining the right to freedom of expression and opinion in other states, as well as in their own."
They closed their airspace to Qatari carriers and blocked the emirate's only land border, a vital route for its food imports. They also ordered all Qataris to leave and their own nationals to return home.
And after Riyadh last week laid down its list of 13 demands for Qatar, the UAE warned the country should take them seriously or face "divorce" from its Gulf neighbours.
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