Captain Charles Ollivon will miss the game after contracting the virus, along with the nine other France players who have tested positive so far.
Les Bleus are top of the Six Nations table after winning their opening games against Italy and Ireland.
A decision on whether the match can be played will be made on Wednesday.
"Ensuring the health and safety of all players and staff is our number one priority," said a Six Nations statement.
"Should the decision be that the fixture cannot go ahead, the match will be rescheduled for the earliest possible date.
"Six Nations would like to wish all affected players, coaches, and support team a speedy recovery."
Scottish Rugby released a statement saying they could be without 10 players should the game be rearranged for another date.
"Any postponement will have an impact on the player release agreement in place with clubs," said the statement.
"We will be working closely with our Six Nations counterparts to press the case for this week's game to go ahead, should it be medically safe to do so."
Ollivon, Brice Dulin, Cyril Baille, Romain Taofifenua and Peato Mauvaka tested positive on Monday.
Mauvaka is the only one of the 10 players to have contracted the virus who did not feature in the matchday 23 for the round two win over Ireland.
The French Rugby Federation said two members of backroom staff were also considered "suspicious cases" after their tests.
The players and staff involved will return home to isolate and the rest of the side will return to training on Wednesday with testing taking place every 24 hours.
Star scrum-half Antoine Dupont, centre Arthur Vincent, hooker Julien Marchand, wing Gabin Villiere, and prop Mohamed Haouas are already isolating after returning positive tests last week.
Head coach Fabien Galthie and assistant William Servat also tested positive earlier this week and have been isolating.
Uncapped players Gaetan Barlot, Thierry Paiva and Cyril Cazeaux have been called up to the squad, along with Baptiste Pesenti and Thomas Ramos.
Scotland are fourth in the Six Nations table after winning their opening game against England before losing to Wales.