Arteta suffered the horror injury just three minutes into Sunday’s goalless draw at Newcastle.
The Spaniard could be out of action until Christmas, according to The Sun.
Everton skipper Phil Neville said: “It’s a massive blow for us because any team would miss a player of Mikel’s quality. But we have an awful lot to play for and there’s nothing to be gained by feeling sorry for ourselves.
“Over the next few weeks we will get the likes of Leon Osman and Steven Pienaar back from injury and Tim Cahill back this weekend after suspension.”