The Belgium international was carried off on a stretcher after being chopped down by Jordon Mutch having previously scored in the 3-1 win over QPR on Monday.
However, Everton's worst fears have been allayed after scans revealed minor ligament damage which should mean Mirallas is available for at least part of the festive period.
"We have great news as we were very worried after the game because it was an action where you feel the ankle is definitely damaged," said Martinez.
"The damage is the least it could be
It is an external ligament in his ankle and the way he is as a quick healer I don't expect him to be out for too long.
"I wouldn't rule him out for any of the fixtures over the Christmas period."
There was more good news on midfielder Leon Osman as Martinez revealed he will not require an operation on an ankle problem which has sidelined him since early December.
"I don't expect Leon to be out for too long," added the Toffees boss.
"When we started to assess the problem, that was the worst-case scenario to go through an operation but he has reacted well enough to the treatment and we are very hopeful he will be okay without an operation.
"Darron Gibson (knee) will be joining the group today and we will assess him after that and James McCarthy (hamstring) is making good progress and both will be assessed before the Southampton game.
"It is a 50-50 situation for both for Saturday."
Martinez also paid tribute to forward Steven Naismith after the Scotland international signed a three-year contract extension which will keep him at Goodison Park until 2019.
"I truly believe he is in the best moment of his career and he has a lot of years at that level in front of him," said Martinez.
"He will get better with games because he is a player who relies on his intelligence and the way he has been performing for us over two seasons has been impressive.
"For him to extend his stay is incredibly good news for us."
Source : PA
Source: PA