Jack aggravated a knee injury after the Rangers midfielder joined up with the Scotland squad last week.
Jack was ruled out of last Friday's defeat by Russia before being sent back to his club ahead of Monday's loss to Belgium.
Gerrard felt the 27-year-old had been overworked by the Scotland coaching staff after doing a double session two days after Rangers' defeat by Celtic.
Jack is now a doubt for Rangers' Scottish Premiership clash with Livingston today.