The 20-year-old landed awkwardly after winning a header in the dying stages of Sunday's 2-1 defeat at Old Trafford and was forced to withdraw from the England squad after Martinez confirmed that the youngster had suffered ligament damage.
"It's a clear injury – not a complicated injury. Obviously, it's a little bit of a setback because you don't want to lose any players but, in John's case, we were very worried in the moment that it happened because those injuries can become a little bit difficult to treat.
"But this one is going to be straightforward and we are already counting down the days for him to come back and we'll make sure he comes back stronger and ready for the final and most important part of the season."
Stones has quickly become a permanent fixture in the Everton back line since his €3.8 million move in January 2013 and started each of the side's last four Premier League games as well as earning a call-up to Roy Hodgson's England squad.
The Three Lions called up Calum Chambers as a replacement but his injury setback is another big blow for Everton and Martinez, who have an ever-expanding injury list with which to contend.
The Merseysiders, sitting in 17th place in the Premier League, are already without Sylvain Distin, who is nursing a thigh problem, as well as Seamus Coleman, James McCarthy and Kevin Mirallas - though Ross Barkley is nearing a return to first-team action after missing the start of the season.