The Republic of Ireland international injured a knee in last weekend's friendly win over Real Betis at Goodison Park and faces a race against time to be fit.
"He is going to be touch-and-go for Saturday," the Spaniard told evertonfc.com. "He has got a little bit of a strain in his right knee. It's something he picked up in the warm-up, and he tried to run it off and get through the game but he couldn't.
"Knowing Darron, maybe he has got a chance for Saturday. But it's a little bit of a concern because he will need treatment and we'll see how that knee reacts over the next 48 to 72 hours."
Gibson has been a key player for Everton since he joined from Manchester United in January 2012, but last season he struggled with a thigh injury for much of the campaign.
Losing him for the season opener would be a blow for Martinez, who begins his Everton reign at Carrow Road.
"Darron's a special footballer. What he brings to the team is quite unique and I think he is one of those players that is at the perfect moment of his career," the Spaniard told evertontv.
"He's ready to take a big role at Everton. To miss any player at this stage of the season would be a real blow.
"He has been working over 60 to 70 hours, and then if we lose him a few days before the start of the season it would be a big disappointment, but we hope that Darron can recover very quickly."
Already ruled out of the trip are the trio of Tony Hibbert and Magaye Gueye - whose injuries are unspecified - and summer signing Antolin Alcaraz (hamstring).
Source: PA
Source: PA