Celtic manager Neil Lennon accused the Scottish Football Association of presiding over an "absolute shambles" after 11 Scotland Under-21 players were instructed to self-isolate.
Celtic midfielder David Turnbull was among three players who tested positive for Covid-19 after returning from Tuesday's European qualifier in Greece, while a further eight players were identified as close contacts.
Lennon questioned why more testing was not carried out after a member of the backroom team tested positive last Sunday before the squad travelled to Athens.
Aberdeen will have three players missing for their trip to face Rangers at Ibrox on Sunday after one tested positive, Livingston confirmed goalkeeper Robby McCrorie had tested positive, and Motherwell lost two players for their 1-1 draw with St Johnstone at late notice.
The players involved were back training with their clubs for two days before positive cases emerged on Friday night and the situation escalated on Saturday morning.
After his team's 2-2 draw with Hibernian, Lennon said: "It's a shambles, an absolute shambles. We give these players in good faith and we get them sent back and it's basically 'you look after them now'.
"There should have been more testing done, especially when there was an outbreak last week.
"We were all tested on Friday and everybody came back negative. These players have gone out of our bubble and into the international arena and are coming back with the virus. It's hard to take.
"It's very difficult to stop players from playing for their country, I'm not sure it's the right thing to do. But what we can ask is the associations look after the players the best way they can."
The SFA declared that the three positive cases would have to self-isolate for 10 days from Friday, and the 10 close contacts, including two staff members, will need to stay at home for 14 days.
A statement added: "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.
A Dons 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."
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."
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. Hibernian defender Ryan Porteous and Ross County goalkeeper Ross Doohan both played on Saturday.
Meanwhile, Albion Rovers' League Two game with Cowdenbeath was postponed after seven players and staff from the Coatbridge club tested positive.
