The Belgium international sustained the injury during the first half of Everton's 1-1 Premier League draw with Liverpool at Anfield last month.
Everton boss Roberto Martinez's initial prognosis was pessimistic, but the Spaniard revealed on Thursday that Mirallas would not need an operation to correct the problem.
"Kevin does not need surgery, just conservative treatment," he said. "We hope to have him fully fit soon.
"Kevin has got a typical sprinting injury. We expect him to be out for a few weeks as well."
Martinez also said that Bryan Oviedo had "reacted well" to having a screw taken out following the broken leg he suffered in January, and there was further good news surrounding Ross Barkley, who is yet to feature this season due to a knee problem.
"On Monday we expect Ross, with the green light from the medical department, to join the group," he added.
"Now it's a matter of getting him match fitness and getting him up to speed. Ross has been working really, really well and I don't expect any setbacks. I expect Ross, from now on, to have a real clear path to get his match fitness back.
"He'll be like a fresh, new player for us."
But Martinez remained cautious when quizzed over Barkley's return to first-team action.
"It depends," he continued. "Sometimes it's a couple of weeks, sometimes it is less. It depends how his body reacts to the work and how quickly he can get the physical element.
"Remember, one of Ross' biggest strengths is his physicality and how strong he is sometimes helps in terms of getting his match fitness.
"But he has been out for a while and we need to make sure we give him the right work now to make sure he is at his very best. His desire and hunger to be in the team is contagious and that is something I want to have with the group.
"From Monday I want him to be part of it and in probably a couple of weeks we should be able to see Ross in the squad."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.