In a statement, the league (LFP) said that "noting the certain absence of 11 Lens players from a list of 30 because of positive RT-PCR tests...it has decided to postpone the game between Lens and Nantes scheduled for Sunday to a later date".
It is not the first time this season a Ligue 1 game has been postponed due to Covid-19. Marseille's meeting with Bordeaux on the opening night of the campaign in August was rescheduled for the same reason.
After that, and fearing an avalanche of postponements, the LFP relaxed its health protocol to ensure games could go ahead as long as at least 20 players from a list of 30 on each team tested negative.
The Ligue 2 game between Grenoble and Nancy scheduled for Saturday was also postponed after 13 Grenoble players tested positive along with five staff members.
Lens and its surrounding region, in far northern France, are currently under a nighttime curfew along with much of the country as part of efforts to reduce the spread of the virus.
France has recorded more than one million cases and close to 35,000 deaths from Covid-19.
Elsewhere, Marseille bounced back from their 1-0 midweek loss away to Olympiakos in the Champions League with a victory by the same margin at Lorient on Saturday.
Argentine defender Leonardo Balerdi headed in from a tight angle for the only goal in the second half after home goalkeeper Paul Nardi was caught underneath a hanging Florian Thauvin free-kick.
Reigning champions Paris Saint-Germain host Dijon later at the Parc des Princes in a game that will be played behind closed doors.
On Friday, Rennes lost 2-1 at home to Angers as their unbeaten start to the season came to an end.