The player is on loan from Barcelona for the season and the Spanish club said on Thursday that tests conducted in the Catalan capital had shown he would be out for "approximately six to eight weeks".
Deulofeu is to recuperate in Spain under the supervision of Barca medical staff and their Everton counterparts.
The forward was injured in Saturday's 4-1 win over Fulham, a result that moved fifth-placed Everton within four points of Premier League leaders Arsenal.
Deulofeu was making his second start of the campaign after being rewarded for a brilliant equalising goal off the bench in a 1-1 draw at Arsenal the previous week.
Everton said after initial tests on Monday that Deulofeu would be out for "a few weeks".