Manager Antonio Conte revealed on Wednesday that as many as eight players and five members of staff had contracted the virus.
A statement released on Tottenham's official website read: "We can confirm that our Premier League fixture at Brighton and Hove Albion, on Sunday 12 December at 2pm, has been postponed following a Premier League Board meeting.
"The Premier League Board took the decision to postpone the game following guidance from medical advisers, with the health of players and staff the priority. The fixture will be rescheduled in due course.
"The club requested the match to be rearranged following a significant number of positive COVID-19 cases among players and relevant staff.
"As with our other affected fixture, against Rennes in the Europa Conference League, we shall update supporters with more information as soon as it is available.
"We should like to apologise to everyone at Rennes and Brighton and Hove Albion and to both their supporters and ours for any inconvenience caused.
"We should also like to thank both clubs for their understanding during these challenging times."
Tottenham, who are fifth on the table, will now have two games in hand after their midweek fixture against Burnley last week was postponed because of snow.
