The Belgium international was substituted in stoppage time during Everton's 2-0 win over Manchester United on Sunday after sustaining the problem, having scored his side's second goal just before half-time.
Mirallas' 43rd-minute strike was his eighth in all competitions in 2013-14, but he will not feature again for the Toffees this term.
"Roberto Martinez today revealed that the Belgian [Mirallas] has a small tear in his groin and will be out for the next three weeks," the club confirmed on their official website.
"He will be sidelined for matches against Southampton this weekend, the visit of Manchester City on 3 May and the last game of the season at Hull City."
Mirallas is expected to be part of Belgium's World Cup squad, although this injury means he faces a race against time to be fully fit.
News of Mirallas' setback will come as a blow to Everton as the Merseyside club look to beat Arsenal to the final Champions League place in the Premier League.