The captain strained his calf shortly before the national team left for Canada, and will be treated by medical staff on tour.
The 23-year-old Stewart joins McInally and Glasgow Warriors pair Fraser Brown and George Turner.
The BT Sport Academy Stage 3 front-rower has represented Scotland at age grade, and was on the call-up list for the Under-20s during the 2015 Junior World Cup campaign. He has also played for the Club XV side.
The 23-year-old began his rugby career with Strathaven, before joining Dalziel and then Glasgow Hawks.
He has made seven appearances for Glasgow this season as well as turning out for Hawks in the BT Premiership.