Fourth-tier Orient tried to rearrange the game but League Cup rules mean that they must forfeit the tie, allowing Spurs to go through to play Chelsea.
Competition organisers the EFL said in a statement: "The Round Three tie scheduled for Tuesday 22 September between Leyton Orient and Tottenham Hotspur could not take place following the issue by Waltham Forest Borough Council of an order preventing the match being played as planned. This followed a number of Leyton Orient players testing positive for Covid-19.
"The EFL Board has determined that in line with Carabao Cup Rule 5.1, the club was unable to fulfil its obligations to complete the fixture by virtue of the Council's order and shall therefore forfeit the tie."
Orient's League Two game with Walsall this weekend has also been postponed as their squad self-isolate.
Spurs will now prepare for four games in eight days, starting with the visit of Newcastle on Sunday.
Jose Mourinho's men then travel to Chelsea on Tuesday, host Maccabi Haifa in Europa League qualifying on Thursday and travel to Manchester United a week on Sunday.
kca/mw