The 25-year-old ruptured his anterior cruciate ligament (ACL) in the opening stages of the Republic of Ireland's World Cup qualifier against Kazakhstan in Dublin on Tuesday night and had to be taken off on a stretcher.
Speaking at Everton's Finch Farm training complex on Thursday morning, Martinez described the results of the scan on the Irishman's knee as "positive", although he remained reluctant to put an exact timescale on how long the recovery may take.
"I was watching the game and straight away I was really disappointed and fearful of the worst but, with the scans [on Wednesday], they were very positive," said the Spaniard.
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Martinez was also quick to deny allegations that Ireland caretaker manager Noel King overused Gibson, who had just returned from a serious injury a matter of weeks ago, by selecting him from the start in the games against Germany and Kazakhstan.
"No, no - if it had been in the 80th minute then you can go down to the detail and say fatigue played a part," he added, "but obviously it happened in the first half an hour of the game and he looked really free in his movement.
"When you watch the action it was such an unfortunate way that the knee couldn't react any other way, it was just an unexpected moment that in football you can't do anything about."
The Everton boss is already looking forward to having Gibson back and fit for selection so that he can continue to build on his promising partnership with James McCarthy for both club and country.
"I think the partnership he showed with James McCarthy during the games was really exciting for everyone," Martinez enthused. "You can see the way he was starting that relationship with James and that is going to be a real important partnership in the future when we see Darron fully fit as we can."