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 the club's website.
"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 added.
"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).
"Tony is recovering really well. I don't think he will be too far away but Saturday is a little bit too early," said Martinez.
"I don't expect him to go too much longer without being available to join the group.
"Antolin Alcaraz is probably two weeks away from being back with the full group.
"Both are progressing well behind the scenes and the same can be said about Magaye. He has been working hard in the last two to three weeks."
Martinez is hoping all of his players return from international duty injury-free.
Phil Jagielka, Leighton Baines (both England), Steven Naismith (Scotland), Marouane Fellaini, Kevin Mirallas (both Belgium), Tim Howard (United States), Seamus Coleman (Republic of Ireland) and Nikica Jelavic (Croatia) are all involved with their national sides, with the likes of Ross Barkley, John Stones, Luke Garbutt, Shane Duffy and Apostolos Vellios playing in under-21 internationals.
"It is frustrating," Martinez said. "You have got players away representing their countries and, in a way, it is always great to carry the name of Everton in international games. But you are just keeping your fingers crossed that we can get through with no injuries. That is always a bit of an anxious time.
"I try to watch all the games. We follow all of them through reports and, for as many as we can, we try to get the live games.
"We keep a close eye on how the players are used and how well they can get through the games.
"For us it is important to get as much information from the matches as possible."