The Scottish football authorities will unveil new enforcement rules tomorrow and have signalled they will “encompass recent breaches”.
Clubs outside the Scottish Premiership have also been told they cannot yet return to training, but relegated Hearts had already done so.
The Joint Response Group has acted following demands by the Scottish Government to instigate penalties for breaches of health and safety guidelines.
First Minister Nicola Sturgeon handed Scottish football a “yellow card” on Tuesday after it emerged Celtic left-back Boli Bolingoli had travelled to Spain and failed to quarantine days before playing against Kilmarnock.
That came after two Aberdeen players caught Covid-19 and a further six were instructed to self-isolate following a night out.
The indiscretions led to four Scottish Premiership matches being postponed and both clubs opened internal disciplinary proceedings while Bolingoli received a police fine, but no punishments were open to the league or governing body.
A statement from the Joint Response Group read: “The JRG has worked to ensure that existing rules will be strengthened to include the provision of sanctions for players who do not adhere to Covid-specific football protocols or government public health guidelines.
“This will encompass recent breaches and further details will be provided tomorrow (Friday).”
The Scottish Football Association has also agreed that the return to training of all clubs outside the Premiership will be delayed until August 24 at least, pending updated government guidance next Thursday.
The delay is to ensure that all clubs are complying with protocols, social distancing, testing and hygiene measures, and that all players and club staff are fully aware of the latest government guidance.