Sexton is now a doubt for Ireland's trip to Scotland later this month, although coach Declan Kidney is not sure exactly how long a lay-off he will endure.
"It looks like a couple of weeks for Jonny, but it would be wrong to try to second-guess the outcome. We'll know more by Tuesday," said Kidney.
"It's been an additional couple of games and we had a few injuries leading into the tournament, but that's the way it goes."
Ireland are already without Simon Zebo, who will miss the rest of the competition with a broken foot.