The Republic of Ireland international came on at half-time in Tuesday's friendly at Tranmere but was withdrawn in the second half.
He will stay behind at the club's Finch Farm training ground with striker Arouna Kone and defender Bryan Oviedo, who are still making their way back from knee surgery and a broken leg respectively.
However, England midfielder Ross Barkley returns to the squad for the match against Premier League newcomers Leicester in Bangkok on Sunday.
"We assessed Seamus' injury this morning," manager Roberto Martinez told evertontv.
"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."
Martinez has confirmed a deal is close for for Anderlecht teenager David Henen as the Spaniard looks to bolster the club's youth ranks.
The Belgian 18-year-old will go into the Under-21 squad once his reported B£1.5million move has been completed.
"It is in the process of being completed," Martinez told the Liverpool Echo.
"He's a young, talented footballer who represents Belgium in the lower teams, in the Under-18s and has had good experience in going to France.
"He is a bright boy and we feel he is something different that we haven't got in the Under-21s so we are hoping he is going to be giving us something different in that group.
"We want a strong group. We have already got talented and very interesting footballers and I think David can fit in really well in that environment."
- Sports & Recreation
- Bryan Oviedo
- Arouna Kone
- Premier League