"Down with the referendum of blood and treason," said a statement from the alliance on the brotherhood's website. "Long live Egypt and its proud people."
Egyptian expatriates have already cast ballots for a constitution meant to replace the one adopted during the presidency of Mohamed Morsi, a Muslim Brotherhood member.
The Egyptian military removed Morsi from office in July amid mounting frustration with policies seen as favoring the Islamic ideologies of the brotherhood, which says the ouster of Morsi was a military coup that violated the spirit of the country's 2011 revolution.
The new constitution was revised last month to change the phrase "civilian rule" to "civilian government."
The phrase "civilian rule" would have prevented religious or military leaders from taking positions of authority in Egypt. The revision was praised by human rights groups because it was seen as less restrictive.
The referendum in Egypt is scheduled for two days beginning Thursday.