Traore, who is on loan from Monaco, sustained the injury in the warm-up to Everton's match with Chelsea on Saturday.
Roberto Martinez admitted it was a big blow for both the club and the player, especially given that the forward previously suffered a similar injury.
Although the Everton boss said that Traore would be sidelined for weeks rather than months, Martinez admitted he was concerned and would not rush the forward back to action.
Martinez told evertontv: "It is going to take a long period of time which at this stage of the season will be a big miss. It will be weeks rather than months.
"It's a really disappointing outcome. He was ready and had been working really hard since he arrived at the club.
"Starting the game at Chelsea was the next target after Swansea and for him to pull his hamstring in the last action of the warm-up was a really disappointing moment.
"We are a little bit concerned. We are working with his parent club and making sure we get the right diagnosis. Lacina was really down after and we need to support him. We will find out over the next 48 hours how we will treat the injury.
"It is a soft tissue injury in the hamstring very similar to a previous injury he had.
"In those sort of injuries, similar to the injury Gerard Deulofeu picked up before Christmas, the soft tissue is an area which needs to be well healed. It is going to take a long period of time which at this stage of the season will be a big miss."
However, the Spaniard reported that Romelu Lukaku is close to returning from an ankle injury.
"Romelu has been working really well and he is looking fresh and ready. We are all very excited to see him back enjoying his football with really top energy levels," Martinez said.