Mirallas sustained the problem in Saturday's Merseyside derby at Anfield, the Belgium international having to come off in the first half of the Barclays Premier League contest, which ended 1-1.
Martinez had already admitted the signs were "not great" with regard to the problem as Everton waited to learn the full extent of it.
And when asked about Mirallas on Wednesday in Russia ahead of his side's Europa League Group H clash with FK Krasnodar, Martinez said: "At the moment it is still a bit early because the inflammation in the area doesn't allow us to get the full extent.
"But clearly it is an injury that will keep him out for a while.
"We are just going to make sure in the next 48 hours we get the clear diagnosis for it."
Along with Mirallas, midfielder James McCarthy and full-back Seamus Coleman are among those to have not travelled with the Everton squad for Thursday's game.
McCarthy has felt tightness in his quads following the match on Saturday, while Coleman, absent for the last three fixtures after sustaining a head injury, is now nursing a soft tissue problem.
However, both could possibly be in contention for Sunday's league trip to Manchester United.
Source : PA
Source: PA