Baines has been linked with Manchester United this past week.
Martinez told Sky Sports News: "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 today.
"We hope that Leighton can be fully fit very, very soon."