The Republic of Ireland international was withdrawn during the second half of Everton's 2-2 friendly draw with Tranmere Rovers on Tuesday.
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"We assessed Seamus' injury this morning," Martinez told the club's official website on Wednesday.
"He will miss the Thailand trip to give proper consideration to his injury, for proper treatment and to remove any chance of aggravating that feeling that he had.
"We don't really know the extent of the injury yet but it is sometimes a little bit of a setback that comes with pre-season preparation and getting a lot of volume into the bodies. Hopefully it is going to be just a minor setback."
Ross Barkley is among the party travelling to Bangkok after an extended break following his involvement at the World Cup, but Arouna Kone and Bryan Oviedo, who are long-term injury absentees, will not make the trip.
Martinez added: "Bryan Oviedo and Arouna Kone have been progressing really well and we want them to carry on working every day in a way that they don't get distracted with travelling - so they won't travel to Thailand.
"It's more a case of trying to get them ahead of where they are. Seamus will miss the trip but Ross Barkley will join the group."