Etihad, which operates four return flights to Doha daily, said the measure will be in place 'until further notice'.
Other carriers from the three Gulf countries are likely to announce similar measures.
The former army chief and now president, Abdel Fattah al-Sisi, along with the new government's allies in Saudi Arabia and the UAE, blacklist the Brotherhood as a terrorist organisation.
Egypt, the Arab world's most populous nation, said on its state news agency that Qatar's policy 'threatens Arab national security and sows the seeds of strife and division within Arab societies according to a deliberate plan aimed at the unity and interests of the Arab nation'.
Egypt is expected to suspend air links with Qatar by Tuesday.
Qatar's Emir Sheikh Tamim bin Hamad Al-Thani (pictured in 2014) attends a Gulf Cooperation Council summit in Doha, Qatar.
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This by itself is a violation of its (Qatar's) sovereignty as a state,' Qatar added.
'We have no further comments for the time being.' It wasn't immediately clear how the cutting of ties would affect Qatar Airways, one of the region's major long-haul carriers, though the airline suspended all flights to Saudi Arabia on Monday.
Abu Dhabi's state-owned Etihad Airways said it would suspend all flights to and from Doha from Tuesday morning until further notice.
It accused Qatar of supporting what it described as Iranian-backed militants in its restive and largely Shi'ite Muslim-populated Eastern region of Qatif and in Bahrain.
Qatar was also expelled from the Saudi-led coalition fighting a war in Yemen.
Gulf countries led by Saudi Arabia fell out with Qatar over its backing of then-Egyptian President Mohammed Morsi, a Brotherhood member.