
The midfielder was one of several absences from David Moyes’ first matchday squad of the summer, with Jarrad Branthwaite, Hayden Hackney and Vitalii Mykolenko also missing.
Everton said Garner had “experienced discomfort in his groin” after the return to training, which took place in Scotland across this week, and would be assessed next week.
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The 25-year-old, who emerged as one of the Blues' star players last season, is the only injury concern so far.
Branthwaite, the club said, was continuing to make “positive progress” from the hamstring injury he suffered against Liverpool in the final weeks of last season.
As previously reported by the ECHO, his minutes are expected to be managed through pre-season to ensure he has time to continue that recovery without putting his body under too much pressure after last season was ruined by injuries.
New signing Hackney had been “successfully integrated” into the squad, Everton said, adding that process would continue next week as planned.
Mykolenko, meanwhile, was with his partner for the birth of their second child.
The Blues won 4-0 thanks to goals from Beto, Thierno Barry, Harvey Foster and Dwight McNeil.