The 26-year-old Spaniard was carried off the field on a stretcher after sustaining the injury to his right knee early in Everton's 0-0 draw at Newcastle United on Sunday.
"He underwent a succession of scans on his knee on Sunday night to ascertain the full extent of the injury, with the results revealing he has no chance of pulling on an Everton jersey again this term," the club said on their website.
Arteta has been one of the key figures in sixth-placed Everton's season, making 31 appearances and scoring seven goals.
His absence will be a huge blow to manager David Moyes, whose squad has already been severely depleted by a string of injuries and they have spent several months playing without a recognised striker.
The club were still awaiting news on Victor Anichebe's fitness after the forward was hurt in a two-footed challenge from Newcastle's Kevin Nolan who was shown a straight red card.
Moyes said his squad lacked the depth to cope with so many injury setbacks.
"Injuries are part of football but what we'll miss is that we don't have the squad or numbers to do it," the manager said on the club's website. "You've got to have the numbers, and that's where our problem comes."
Moyes had already lost Yakubu Aiyegbeni for the season with a ruptured Achilles, while fellow striker James Vaughan is not expected back until the middle of next month because of a knee injury.
Midfielders Leon Osman (stomach strain) and Steven Pienaar (hamstring) missed the Newcastle game.
"We have had players out of position before but not this much out of position," Moyes was quoted as saying by British daily The Guardian. "We are close to breaking point."
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