Dundee United have been trying to manage Covid-19 issues ahead of their trip to Ibrox on Saturday and St Johnstone were without Chris Kane during their 2-0 defeat by Rangers on Wednesday after a member of his household tested positive.
Kane will have to self-isolate for 10 days under new rules, whereas before he would have been free to play if he returned a negative PCR test.
The new wave of the pandemic is set to hit during Scottish football's busiest period, which immediately precedes a two-week winter break for the top flight.
Livingston manager David Martindale, whose team host Ross County on Saturday, said: "If you were asking me what would I do right now - I would shut the league down for two weeks. I would have a circuit-break and go again.
"I don't believe it's fair on teams even when they meet the criteria of 13 players, so many over-18, two goalkeepers. I don't believe it's fair for the competition and the product.
"A lot of these Covid issues are unrelated to the football club. I've got a member of staff who lives with her mum and she phoned in today, she can't come in. She's not got Covid but her mum has.
"My chef and one of the ladies at the front desk, they had a staff night out last week - they are isolated from the players - they went for a meal and two of them have potentially got Covid.
"Is that going to drip-feed into the football department very soon? I would imagine so.
"My daughter is at school so how many households is Georgia mixing with on a daily basis? Is Covid potentially going to come into my house, into Livingston Football Club? I think it is. Is there anything we can do to stop it? I genuinely don't think there is.
"So we need to be clever on how we approach this. I think it's going to have a massive impact on Scottish football over the next couple of weeks."
The cinch Premiership winter break, which starts after the Edinburgh derby on January 3, offers a potential opportunity to delay the festive schedule.
Martindale said: "We are booked to go away somewhere but is that really why you wouldn't do it? It isn't, is it?
"Is it fair that Dundee United could potentially be going into a game at Ibrox, and I don't know the situation, with six or seven players missing?
"Dundee United are just the start. This is going to affect us all and I think it's going to get worse as the days and weeks go on.
"Could we go on a circuit-break and start two weeks earlier in the winter window? It's easy for me sitting here saying that, I understand the logistics with the SPFL and SFA, but for me that is an option.
"I don't think it's fair that, let's say, a week down the line we take this decision and three or four clubs have had disappointing results due to the Omicron variant. I don't think that's fair.
"There is nothing as a football club we can do to stop this happening."