A total of 24 defendants attended the hearing in Abu Dhabi, WAM state news agency reported, saying that the session was attended by families of the defendants as well as by representatives of civil society and the media.
The so-called "Muslim Brotherhood cell" comprises 10 Emiratis and 20 Egyptians, including six who remain at large.
The judge appointed a three-member medical committee to perform check ups on some defendants, WAM said, adding that he adjourned the hearing until November 12 to allow more time for lawyers to call in witnesses.
Prosecutor Ahmed al-Dhanhani accused the group of having "established and managed a branch for ... the international organisation of Egypt's Muslim Brotherhood, without a permit."
The founders set up an administrative structure aimed at recruiting members for the Muslim Brotherhood, strengthening its presence in the UAE and maintaining allegiance to the main party in Egypt, he said.
The group also "raised money through donations, Zakat (Islamic alms), and membership fees to support" the Brotherhood, he added.
The Egyptian defendants, including doctors, engineers and university professors, were arrested between November 2012 and January 2013, according to Human Rights Watch.
The UAE has not seen any of the widespread pro-reform protests that have swept other Arab states. However, authorities have boosted a crackdown on dissent and calls for democratic reform.
The Gulf emirate strongly supported the July 3 ouster by the Egyptian military of the country's first democratically-elected president -- the Muslim Brotherhood's Mohamed Morsi.
Ties between the UAE, where political movements are banned, and Egypt were severely strained during Morsi's year in power during which the Gulf state arrested a number of Egyptian residents.
The top UAE court in July jailed 69 Emirati Islamists for up to 15 years each on charges of plotting to overthrow the government, at the end of a mass trial criticized by rights groups.
They were part of a group of 94 defendants, including 13 women.
Prosecutors said the accused were linked to Al-Islah, a group with ties to the Muslim Brotherhood.