The tiny Gulf nation's expulsion of the Brotherhood, branded a terrorist organisation by Egypt, Saudi Arabia and the United Arab Emirates, signals it is moving to mend a diplomatic rift triggered by its support of the group.
Analysts described the move as a political victory for Egypt's current leadership.
Minister of Interior Mohammed Ibrahim said that Qatari authorities gave Brotherhood leaders one month to leave the country, and reporters for the Doha-based Al-Jazeera Egypt channel two months to leave.
A number of the group's senior members and allied clerics had already said yesterday that they would leave "to avoid embarrassing" Qatar, which suffered severely strained relations with Egypt and other Gulf countries for hosting the Brotherhood.
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A Brotherhood member in Qatar, who spoke on condition of anonymity because of concerns for his safety, said the Qataris conveyed to them that they were under constant pressure led by Egypt to serve Egyptian arrest warrants for the Islamists.
He said he will travel to Malaysia while other members will be travelling to Britain or Turkey.
El-Sissi led Morsi's ouster after millions of protesters rallied to demand his resignation last summer.
The head of a Brotherhood-allied Egyptian Salafi party living in Qatar said that Egyptian Islamists there know the country has been under pressure to expel them and that Cairo has been encouraging countries to consider them just as dangerous as brutal extremists who have taken over swaths of Iraq and Syria.
"Egypt wants to brand the Brotherhood with the stamp of the Islamic State group," Ihab Shiha said by telephone, adding that he himself was not asked to leave the country.