Mourinho posted a video on his account of his staff waiting for news with a message which read: "We still don't know if we play. Best league in the world."
The Premier League confirmed the decision to postpone the game was taken following a meeting.
"Fulham lodged a request with the Premier League Board to rearrange the fixture following a significant rise in positive Covid-19 cases, as well as a number of players showing symptoms today," it said in a statement.
"The Premier League board has consulted its medical advisers and the decision to postpone the game has been taken as a precaution and with the health of players and staff as the priority. The group will now be re-tested immediately."
West Brom boss Sam Allardyce voiced support for a "circuit breaker" in the Premier League on Tuesday.
But Manchester United boss Ole Gunnar Solskjaer, whose side beat Wolves to climb to second in the table, called for the competition to continue.
Despite the rising number of cases across the English top-flight, the Premier League said it intended to continue playing.
"With low numbers of positive tests across the overwhelming majority of clubs, the Premier League continues to have full confidence in its Covid-19 protocols and being able to continue to play our fixtures as scheduled," its statement added.
Fulham confirmed the postponement of their match against Spurs followed "a number of the club's players and first-team staff returning positive results from the most recent Covid-19 tests this week".
It added: "This decision follows discussions with the Premier League and advice from Public Health England."
Premier League leaders Liverpool are due to travel to Newcastle for Wednesday's late match.