The 26-year-old suffered a hamstring injury after scoring in City’s 2-0 victory at the DW stadium against Wigan on Wednesday.
Milner is also expected to be a doubt for next week’s Champions League fixture against Borussia Dortmund as well as the derby clash at the Etihad stadium with Manchester United.
This will come as a blow to the player as his return to action on Wednesday night was only his second appearance since suffering a similar injury earlier in the season.
The player had just hit a good run of form for the side and was looking to consolidate his side’s unbeaten run in the Premier League.
The England international played a key role in City’s 6-1 demolition of United at Old Trafford in the first derby day meeting of last season so his influence upon this fixture will be a huge loss.
“James is out for Saturday. We will try to recover him for next Sunday but we don’t know,” Mancini told Sky Sports.
“He played against Chelsea and played very well. He came back after injury, now he played 20 minutes and had a hamstring injury.
“We are disappointed because James was in good form in this moment.”
City will be looking to improve upon their dismal record against Everton with the Toffees winning eight of the past 10 Premier League matches between the two clubs.
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