The 23-year-old Ivorian striker, who joined the Toffees on loan from French club Monaco in January, suffered a recurrence of a hamstring injury against Chelsea last month.
It was initially feared that Traore may have to sit out the rest of the campaign, but further tests have revealed that he will be back in action by May.
"He should be back in the next seven to eight weeks so it's not the end of Lacina at Everton," Martinez told the Liverpool Echo.
"We're excited about that and he's delighted. He was in the dressing room devastated at Stamford Bridge after the warm-up.
"Now he wants to show he's ready to help the team and if he can participate in the last two or three weeks of the season, it will be a major bonus."
Martinez added to evertontv: "We've seen the specialists and we're now ready to proceed with what's going to be the best treatment for Lacina, and it's not going to be surgery, which is fantastic news."
Meanwhile, Martinez has not given up hope of having captain Phil Jagielka back to face Arsenal in Saturday's FA Cup quarter-final at the Emirates.
The England centre-back was ruled out of Wednesday's friendly against Denmark because of a hamstring injury which caused him to miss last weekend's win over West Ham.
"With Phil, you can never rule him out," added the Toffees boss. "From a medical point of view, he should be missing the game against Arsenal - I was probably looking more at the Cardiff game (on March 15).
"But knowing him and how he's reacted to this similar injury that he's had in the past, he could heal a lot quicker.
"I'm not going to rule him out and we're going to give him as much time as he needs to make a final decision.
"In a way, it's good that he's behind-the-scenes here at Finch Farm and he hasn't got the game with the national team.
"That could give him a small percentage (chance) to be fit for the weekend. We'll see how this week unfolds and make a final decision closer to the game."