Aberdeen’s game against Hamilton tomorrow is expected to be cancelled.
And Celtic’s clash against St Mirren is also likely to be off.
It comes as the First Minister said “we shouldn’t expect to see Celtic or Aberdeen play over the course of the coming week”.
The Dons and Hoops are also set to meet at Parkhead this weekend.
Eight Aberdeen players are in self-isolation after they visited a city bar on August 1, with two subsequently testing positive for Covid-19.
Celtic player Boli Bolingoli has also apologised for travelling to Spain, before returning and playing for the Hoops against Kilmarnock on Sunday. Bolingoli made the trip without Celtic’s knowledge and should have quarantined on his return.
Both incidents have cast doubt on whether the two-week-old Premiership season can continue.
The First Minister added: “I don’t order the football authorities to do anything.
“We’ve had discussions this morning, given the circumstances, I don’t expect to see the two clubs play football this week.
“SFA and SPFL should be getting their house in order and make these decisions.
“Clubs and footballers need to understand that they have a responsibility to not make the wrong decision.
“I don’t want the football season to be put in jeopardy, it’s the fans that will be let down.
“Hopefully this is a turning point for football.”
National Clinical Director Jason Leitch added: “The football authorities are taking this very seriously, they did not try to defend the clubs or the players.
“I am not pre-empting our decision which will be made later on.
“This young man went to Spain, which is a high-risk place and then went to work, which put his team and opposing team at risk.
“There needs to be an implication for him, his team and everyone he has been in contact with.”
When asked if she regrets giving football the go-ahead as early as she did, the First Minister said: “What I regret is that football players can’t live up to their responsibilities.
“We dispatched Jason to talk to all the managers and captains to football clubs to discuss the importance of this.
“This Celtic player flagrantly breached the rules.
“We can’t have privileged football players deciding they are not going to bother.
“I want to get to a situation where clubs and players live up to their responsibilities.
“I don’t want fans to pay the price for this or clubs and players who are listening to the rules.
“We have spoken to clubs this morning about how they will set their houses in order.
“This situation is now unacceptable.
“We will be setting out conclusions later on this afternoon.
“You can’t expect Celtic and Aberdeen to play later this week.
“This is a yellow card for football.”
Bolingoli came off the bench during his side’s 1-1 draw against Kilmarnock on Sunday.
This morning, Celtic released a statement “unreservedly” condemning his actions.
It said: “It is difficult to imagine a more irresponsible action in current circumstances and we find it beyond explanation. The club will take immediate action through our own disciplinary procedures.
“Celtic are in touch with every SPFL club today, and with all relevant authorities, to apologise for the fact that one of our employees has created so much additional difficulty through his actions.
“All of our playing and backroom staff have been tested twice for Covid-19 since this incident and all, including the player in question, have tested negative. While this comes as a relief to all concerned, it in no way diminishes the seriousness or stupidity of the player’s actions.”
The eight Aberdeen players were told to self-isolate after two tested positive for Covid-19 after a night out at a bar in the city.
As a result the Dons game against St Johnstone was called off.
A statement released by the eight players read: “First and foremost we would like to apologise to every AFC fan, the manager, everyone at the club, the football authorities, the First Minister, all healthcare workers along with everyone else that has worked tirelessly around the clock to get the country, and in particular football, back up and running again.
“We, as a small group of players, made a huge error of judgement last weekend by thinking it was ok to visit a city centre venue together.
“None of us could have foreseen the escalation of Covid-19 cases in the Grampian area, nor did we deliberately attempt to flaunt or disobey Government guidelines which we all must adhere to, or indeed the clear guidelines set out by the club.”