Mirallas limped off against Manchester United on Sunday, after scoring the Blues' second goal in the 2-0 win at Goodison Park.
The Belgian has a small tear in his groin and will miss the matches against Southampton on Saturday, the visit of Manchester City the following weekend and the final game of the season at Hull City.
Everton are currently one point adrift of Arsenal in the race for the fourth and final Champions League berth.
Mirallas had been in excellent form in recent weeks, scoring three goals in four games to help keep the Toffees in close pursuit of the Gunners.
Everton manager Roberto Martinez admitted losing Mirallas was "a real disappointment", but he remained confident that the Belgium international will be fit in time for the World Cup finals in Brazil.
The Toffees boss told evertontv: "Kevin's scans came back and they have revealed a small tear in his groin.
"He is going to be out for the season, which is a real disappointment and a shame because he was in a phenomenal moment of form.
"But the memory we have of his performance against Manchester United is a terrific image. The way he took his goal and how he was a dynamic force throughout the game, it was an outstanding performance.
"It's a great way to finish the season if it's the last game he is going to be involved in this campaign.
"It is not a major injury. It could be anything up to five or six weeks, and that's looking at the worst-case scenario.
"The most important aspect now is that we get him fully fit and ready to participate with Belgium in the World Cup."
Martinez also revealed that centre-back Sylvain Distin is unlikely to be fit for Saturday's game against Southampton because of a hamstring injury.