Leyton Orient said it has informed its recent League Two opponents and Tottenham of the positive cases, and that it will make a later announcement regarding Tuesday's game.
'Leyton Orient's priority is the health and well-being of its players and staff.
The players will now follow the self-isolation guidelines set by the British government. Click the link in the orange box above for details.
The two sides are due to meet at the Banks's Stadium on Saturday in the third fixture of the current League Two season.
A statement released by Orient on Monday explained that after Covid-19 testing was conducted following their game against Mansfield Town on Saturday, the club received formal confirmation that "a number" of first-team members had tested positive for the virus.
Tested positive Manchester City’s Ilkay Gundogan
"At this time, the club will make no further comment".
There is no protocol in the EFL competition regulations for this eventuality, in terms of whether the match should be forfeited or rescheduled.
The English Football League (EFL) said it was waiting for the outcome of the discussions between the club and Public Health England before taking any action.
The fourth round of the EFL Cup is due to take place next week and that leaves no possible dates for the match to be played. As is consistent with government guidance, any member of staff who tests positive or begins to experience symptoms will be required to self-isolate.
'The Breyer Group Stadium and training ground facilities will be closed until further notice'.
The match-worn shirts from the Carabao Cup third-round tie will be signed and auctioned in aid of the JE3 Foundation, established in honour of a player who made 276 Spurs appearances between 1990 and 2000 and died of a cardiac arrest aged 49 a year ago.