Thirteen first-team players and staff have tested positive for the virus, leading to Thursday night’s Europa Conference League clash with Rennes being called off.
And now Sunday’s trip to the Amex Stadium will not go ahead after the club’s request for a postponement was accepted by the Premier League club.
A statement read: "We can confirm that our Premier League fixture at Brighton & Hove Albion, on Sunday 12 December at 2pm, has been postponed following a Premier League Board meeting this afternoon (Thursday).
"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 Stade Rennais 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 Stade Rennais and Brighton & Hove Albion and to both their supporters and ours for any inconvenience caused."
Next Thursday's Premier League match at Leicester also appears to be in doubt not only because of Spurs' situation, but because the Foxes are gripped by Covid-19 as well.
The postponement of further games is going to cause significant scheduling problems for Tottenham, having already had a Premier League game with Burnley called off because of snow.
Discussions regarding the rescheduling of the game with Rennes are ongoing with UEFA, with rules stating there is a December 31 deadline for group games to be completed, but it is understood there could be some room for manoeuvre on that as Spurs have a packed domestic schedule before then, while Rennes go on a winter break on December 22.
However, the French club have not taken the postponement of Thursday's game well.
They accused Spurs of causing "London fog" by refusing to tell them how many cases they had and informing them in the afternoon that the game would be played, only to call it off an hour after they had arrived in the capital.
The Ligue 1 club, who returned to France on Thursday morning, later said they "hope the interests of the club will be respected" regarding a possible rearrangement.
Their domestic season is due to be halted for a winter break on December 22 and they hinted they have no intention of playing after then.
A statement read: "Stade Rennais FC hope that the interests of the club will be respected given the important sporting deadlines that await the Rouge et Noir this December."
Premier League bosses wrote to all clubs on Thursday, calling for a step up in Covid safety measures.