Clubs are seeking answers from the Scottish Football Association after 11 Scotland Under-21 players were instructed to self-isolate.
Celtic midfielder David Turnbull is among three players who have tested positive for Covid-19 after returning from Tuesday's European qualifier in Greece.
Aberdeen will have three players missing for their trip to face Rangers at Ibrox on Sunday after one tested positive.
Livingston manager Gary Holt confirmed to BBC Radio Scotland's Sportsound programme – before his team's game against St Mirren – that on-loan Rangers goalkeeper Robby McCrorie had tested positive.
Motherwell also lost two players for their game against St Johnstone.
Rangers had goalkeeper Brian Kinnear plus Glenn Middleton and Nathan Patterson in the squad but none of the players have been in Steven Gerrard's first team this season.
The players involved were back training with their clubs on Thursday and Friday before positive cases emerged on Friday night and the situation escalated on Saturday morning.
An SFA statement read: "Following the return of the Scotland Under-21s squad on Wednesday, the Scottish FA has been informed that three players have since tested positive for Covid-19 during their routine pre-match testing at their respective clubs.
"A meeting involving the Scottish Government's Covid experts took place this morning and after reviewing all relevant information from the under-21 team manager and Covid officer, they identified a further eight players and two staff members considered to be close contacts.
"As a result, the three positive cases will require to self-isolate for 10 days from November 20, and the 10 close contacts to self-isolate for 14 days from November 20.
"The close contacts were established using aircraft and bus manifests, in adherence to government protocols that consider close contacts to be two rows either side of a positive case."
Aberdeen have lost Ross McCrorie, Connor McLennan and Lewis Ferguson for games against Rangers, Hamilton and St Mirren.
The Dons confirmed that one asymptomatic player had tested positive and another two had been identified as close contacts.
A statement added: "No other members of the first team or coaching staff at Cormack Park have tested positive, either during this week's routine testing, or in fact since August.
"From the outset the club has diligently followed the strict protocols outlined by the Joint Response Group and with a regular testing regime and stringent safety measures in place aimed at minimising any potential risk, this is a hugely frustrating situation for all at AFC.
"With three first team players now missing in what is a crucial week for the club, these developments will have a significant impact upon the integrity of its preparations, and it will be seeking urgent assurances from the Scottish FA to ensure its players remain safe whilst on International duty."
Celtic stated they would give every support to Turnbull after confirming he had tested positive.
Turnbull's former Motherwell team-mates, Allan Campbell and Barry Maguire, were ordered to self-isolate despite testing negative following their return to Scotland.
A Well statement read: "We were first notified of the potential need to exclude Allan and Barry at 9:30pm on Friday night. They will now be obliged to isolate for 14 days.
"As a result of what has happened, we will write to the Scottish FA on a number of points on which we believe urgent answers are required."
Hibernian defender Ryan Porteous and Ross County goalkeeper Ross Doohan were both named in their teams' starting line-ups after playing in Athens.
Meanwhile, Albion Rovers' League Two game with Cowdenbeath has been postponed after seven players and staff from the Coatbridge club tested positive.
