Racing 92's president Jacky Lorenzetti said he "did not know" how the club would be able to play Exeter in the European Champions Cup final in just over two weeks after shutting down on Thursday because of a coronavirus outbreak.
Racing had closed their training centre "for five days minimum" and placed their professionals in isolation, "from this morning", the club said in a statement on Thursday.
The club said there were nine positive tests but did not say whether they concerned players or members of the coaching or medical staff.
"Tests carried out on the group on Wednesday morning have revealed several positive cases," the club said.
Racing, who lead the French Top 14 after three rounds, were due to visit to La Rochelle on Saturday, but the game has been postponed "to a later date" the league said.
The club said "new tests will be carried out next week" ahead of a league match against Toulouse on October 10 and the Champions Cup final on 17 October in Bristol.
"I don't know how we will be able to play next week in any case without training, then the European Cup. It's a hard blow, but we'll deal with it," club president Jacky Lorenzetti told French radio.
Racing have won their opening four matches of the season and saw off English club Saracens 19-15 in the semi-final of the European Champions Cup to earn the right to face Exeter.
The English side beat Toulouse 28-18 in the other semi-final.