Tottenham’s trip to Brighton and Hove Albion on Sunday is also in doubt.
Manager Antonio Conte revealed on Wednesday that as many as eight players and five members of staff had contracted the virus.
A statement on Tottenham's official website read: "We can confirm that our UEFA Europa Conference League Group G home fixture against Stade Rennais will not take place tomorrow after a number of positive COVID-19 cases at the club.
"Discussions are ongoing with UEFA and we shall provide a further update on this fixture in due course.
"Additionally, following discussions with the Health Security Agency (formerly Public Health England) and DCMS advisers, the club has been advised to close the first team area of its Training Centre at this time, in the interests of the health and safety of players and staff.
"All other areas of the Training Centre remain operational."
Speaking earlier on Wednesday at a pre-match news conference, Conte said: "Eight players and five members of staff [have tested positive]. But the problem is that every day we're having people with COVID, people that yesterday weren't positive and today are and we're continuing to have contact with. It's a serious problem.
"Today another player and another member of staff positive. Tomorrow, who? Me? Another member of staff? I want to speak about football. This is not a good thing for you, the fans and staff.
"Everyone is a bit scared, we all have families. I ask why? Why? Yesterday we trained and two positives, today we trained and after another two positives. Who next? It's not right, we're going home to our families.
"We had 11 players available for the match and by the end of the training session today one of the players who would start tomorrow is now positive. It's scary. We're all having contact."
