The club informed the SPFL it was unable to fulfil its match against Edinburgh Spartans in the Premier Sports Cup.
All Falkirk Football Club staff have been sent home as a precaution.
Several players tested positive, and others were deemed to be close contacts, leaving the club with no option but to forfeit the Round 1 group stage tie. City were awarded a 3-0 victory.
A club statement said: “We continue to liaise with the authorities regarding future fixtures, however as a precaution all Falkirk Football Club staff have been sent home.
“Our priority remains the safety and wellbeing of our players and staff and we will keep supporters updated as matters develop.”
An SPFL spokesman confirmed the game had been forfeited.
He said: “Consistent with previous announcements in respect of similar issues in the group stage of this competition, any team unable or unwilling to field a team in a Premier Sports Cup Round 1 group stage tie, will forfeit the match on the basis of a 3-0 defeat.”And he added: ““We wish the affected players at Falkirk all the very best in their recovery and will continue to liaise with the club in the coming days, ahead of their next scheduled Premier Sports Cup match against Ayr United on Saturday July 24.”
Edinburgh City confirmed that all supporters who have purchased a match ticket or live stream will be refunded automatically.