The Bosnia midfielder was forced off just 12 minutes after coming on in Wednesday’s testimonial for Wayne Rooney at Old Trafford.
It’s a hammer blow with the start of the season just a week away.
The 23-year-old tweeted: “6 months out! #devastated,”
Besic, who joined the Toffees from Ferencvaros for £4m in the summer of 2014, has been blighted by injuries during his two years at Goodison Park.
Last season a hamstring injury sustained against Chelsea in September sidelined him for four months.