Sexton sustained a hamstring problem and McCarthy knee ligament damage in Sunday's 12-6 defeat by England and team manager Mick Kearney announced that they will miss the trip to Edinburgh.
"Jonny's scan revealed a grade two hamstring injury. Progress has been good so far, but it's too early to say when he will return to play," Kearney said.
"Mike has hurt the medial ligament of his right knee. It's quite sore and he will be in a brace for two weeks. A further review will take place in two weeks."
Ireland received more positive news on the remaining injuries they incurred during a brutal clash at the Aviva Stadium.
Centre Brian O'Driscoll, full-back Rob Kearney, flanker Sean O'Brien and lock Donnacha Ryan are at varying degrees of fitness, but all should be available to face Scotland.
"Brian had a recurrence of the soft tissue injury in his good ankle. Scans revealed no structural damage and he will do non-contact training today," Kearney said.
"Donnacha Ryan suffered a lower back muscle strain. Scans have excluded structural damage but he's quite sore and won't train this week. He'll be reassessed at the weekend and at this stage he has a good chance of being available against Scotland.
"Sean O'Brien has recovered well from his stiff neck and tight hamstring and will train today.
"Rob is fine. He had a slight dead leg but trained fully today."
- Sports & Recreation
- Rob Kearney