Mirallas was carried off on a stretcher during the first half of Saturday's Merseyside derby after pulling up with a hamstring problem.
The Belgian was clearly in pain as he left the field, although a full diagnosis of the injury to his right leg has yet to be made.
Everton are hopeful Mirallas can make a swift recovery, but Martinez concedes that the 26-year-old could be facing a lengthy spell on the sidelines.
He told the club's official website: "These type of injuries, sometimes you need over 48 hours for the inflammation to go down.
"We had a few scans and we are going to carry on today [Tuesday]. It isn't a straightforward diagnosis but obviously the signs are not great.
"We are going to make sure we are clear with the problem. It's not normal when Kevin Mirallas feels something like that and has to come off in the game. We know then that it is something serious.
"We need to make sure we get the full report before we know exactly what is wrong with Kevin.
"He has always been a very fit boy who is always ahead of schedule and we hope this time it is going to be exactly the same."
Mirallas had made an impressive start to the campaign, making the timing of his injury all the more frustrating for Everton.
Martinez added: "His game has gone from strength to strength and the way he had started the season had been really positive.
"He was scoring goals and being a real threat in everything we do going forward.
"We are going to miss him so that is why it is so important that the medical team work well with his rehab and make sure that when he comes back, he comes back refreshed and stronger.
"We have plenty games left for him to be as influential as he has already this season."
Everton are set to make late decisions on whether to include recent injury victims Seamus Coleman, Sylvain Distin and Steven Pienaar in their squad for Thursday's UEFA Europa League match at Krasnodar, a fixture Mirallas will definitely miss.
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