A statement from Egypt's president said that one of the envoys, Essam el-Haddad, presidential adviser on foreign affairs and international cooperation, was carrying a letter from President Mohammed Mursi to UAE President Sheik Khalifa bin Zayed Al Nahyan.
The statement did not disclose the contents of the letter. It said el-Haddad will also meet officials in Dubai and Abu Dhabi.
There is a total ban on political parties and groups in the tightly-controlled Emirates.
The UAE's Al-Khaleej newspaper had yesterday reported that the 11 Egyptians were arrested last month for allegedly collecting security information about the country, holding secret meetings, recruiting members and sending large amounts of money to Brotherhood leaders in Cairo.
Envoys are expected to discuss relations between the two countries, which have soured since Egyptian presidential candidate and former Prime Minister Ahmed Shafiq flew to the UAE soon after his narrow defeat to Mursi in last year's presidential elections.
Litigation against Shafiq followed his departure with a number of investigations and court cases accusing him of corruption during his long political career under Mubarak.
News media in the two countries reported accusations about alleged conspiracies against each other, including rumours of a plan to kidnap Mursi and take him to the UAE. The rumours peaked when thousands of Egyptians demonstrated in front of Mursi's palace last month, protesting against a draft constitution and a presidential decree giving the president wider powers.
In September, Dubai's police chief, Lieutenant General Dahi Khalfan Tamim, warned of an "international plot" to overthrow the Gulf governments by Islamists inspired by the rise to power of the Muslim Brotherhood in Egypt.
The UAE has not faced street protests in the Arab Spring upheavals, but authorities have stepped up arrests and pressure on groups including an Islamist organisation, Al Islah, accused of undermining the country's ruling system.
Cairo: Two senior Egyptian officials today flew to the United Arab Emirates to discuss the arrest of 11 Egyptians accused of forming a Muslim Brotherhood cell in the Arab country, Cairo airport officials said.
First Published: Wednesday, January 02, 2013, 22:14