The 6ft 8in striker injured his hamstring in the warm up prior to Saturday’s game with Chelsea.
The injury is set to be properly diagnosed in the next 48 hours, and if he requires surgery then the striker will have to return to parent club Monaco for treatment.
‘The injury can be solved by conservative treatment or it can involve surgery – that is a massive decision,’ said Martinez.
‘Depending on what route we are going down is going to have certain consequences. It could mean Lacina could play for us again or if he can’t – it’s a bit too early.
‘You get to a point where if it is only going to be a matter of three or four weeks we want Lacina to be here until the end.
‘If it is going to be any longer than two or three months then the loan period is over.’
The 24-year-old joined the Toffees on loan for the remainder of the season in January, having only just completed a big money transfer to Monaco.
Traore was already suffering with an existing hamstring injury upon his arrival.
He has made one appearance for Everton so far, scoring in the 3-1 win over Swansea in the FA Cup on February 16.