The England left-back was missing with a hip injury as his team-mates won 3-1 at Blackburn in their latest pre-season friendly.
But Martinez, who this week said there had been no recent offer for Baines from Manchester United or anyone else, expects the player to be fit to participate across the Atlantic.
He told Sky Sports News at Ewood Park: "I don't think he's going to be out too long.
"He's going to travel with the team, so if I thought he didn't have a chance to participate in the games in the USA then it wouldn't be right for him to travel.
"At the moment, bearing in mind he recovers quite quickly, it was just a precaution we took with him toady.
"We hope that Leighton can be fully fit very, very soon."
Everton's International Champions Cup campaign begins against Juventus in San Francisco on Wednesday, with further games in Los Angeles and Miami to follow.