The full-back had medical exams on his injured right leg on Wednesday but was told he will not be able to play again for 10 days.
Masi, who plays for Viadana, told the www.federugby.it website: "I can return to training only in about 10 days.
"I certainly will not be able to play in Paris but I hope I will have recovered in time to play Scotland on March 6.
"I am gutted, I had never been in a better physical and mental condition and I was enjoying myself in training as well as in the game."
There are also doubts over the Dallan brothers Denis and Manuel.
Winger Denis has a problem with his left shoulder while centre Manuel injured his right ankle against England at the weekend.
Denis was able to train on Wednesday and should play while it is expected a decision will be taken on Manuel before Thursday when coach John Kirwan hopes to name his squad.