The veteran keeper is also out of Brazil's squad for this month's friendly internationals.
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Liverpool haven't detailed the injury, but it has been announced Alisson will be sidelined for the coming weeks.
Giorgi Mamardashvili will be between the posts today at Falmer stadium.
Hugo Souza has been called up by Brazil boss Carlo Ancelotti to replace Alisson for their friendlies against France and Croatia in the United States on 26 and 1 April respectively.