Izzat, the secretary-general of the Islamist movement's Guidance Office, was detained on 22 May as part of a crackdown on the Brotherhood a few days before a referendum on a constitutional amendment introducing presidential elections with more than one candidate.
He was released late on Saturday, said an official in Cairo on Sunday.
A Brotherhood official on Sunday denied there was a deal with the government to release key members of the movement who have been detained for months.
"The announced movement's position to participate in the election is in favour of the nation and the people," said Brotherhood General Adviser Muhammad Mahdi Akif.
The Brotherhood, which is Egypt's largest opposition group but which the government refuses to recognise, had called for a boycott of the referendum because of the conditions limiting independent presidential candidates.
Because of the restrictions, the Brotherhood does not have a candidate among the nine opposition politicians challenging President Hosni Mubarak, who is seeking a fifth six-year term in the elections on 7 September.
But the Brotherhood, its eyes on parliamentary elections in November, has advised its members to take part in the presidential elections and to vote for the candidate of their own choice.
Izzat, who is among the top four members of the Islamist movement, was the most senior Brotherhood member detained in a crackdown which began in March, when the movement started a series of street protests for political reform.
Another leading Muslim Brother, Issam al-Irian, remains in detention.
Izzat paid bail of 2000 Egyptian pounds ($350) and could still face charges, such as belonging to an illegal organisation, the official sources said.