Gibson had to be stretchered off in the first half of his nation's 2014 FIFA World Cup Brazil™ qualifier against Kazakhstan on Tuesday.
Scans revealed that he had ruptured an anterior cruciate ligament and Everton subsequently announced that he would have to undergo surgery.
However, Martinez is confident that the 25-year-old former Manchester United player will return to action before the season is over.
"It was a real disappointment on Tuesday night," said the Spaniard. "I was watching the game and straight away you could see it was an innocuous incident and that is normally when you pick up really bad injuries.
"I was really fearful of expecting the worst, but with the scans on Wednesday we are very positive now. It is an ACL, but the whole structure of the knee is perfectly fine and it is going to be straightforward surgery.
"I'm looking forward to seeing him back, hopefully this season, and that in a way was good, positive news taking into consideration what it could have been."
Everton host Hull City in the Premier League on Saturday.