The Old Firm match between Celtic and Rangers on January 2 is due to be played with only 500 in attendanceCeltic and Motherwell have called for the Scottish Premiership winter break to be moved forward to avoid fixtures being impacted by capped capacities.
First minister Nicola Sturgeon has announced outdoor sporting events can have a maximum of 500 people attending from 26 December for three weeks amid a rise in Covid-19 Omicron cases.
Hearts have also told fans they are "exploring all options".
Three full fixture cards are scheduled during the period.
The winter break for the Scottish top flight is due to commence on 4 January, with Hibs the first team back in Scottish Cup action on 20 January.
"Everyone at Celtic recognises the difficulties presented to society by the current pandemic and the health and safety of all must always be our priority," said Celtic, whose fixture on Wednesday with St Mirren is now in doubt with the Covid-hit Paisley club requesting a postponement.
"The game owes it to supporters to explore all opportunities to maximise the prospect of all supporters being able to attend matches and support the game they love."
Motherwell chief executive Alan Burrows said the latest measures were "incredibly frustrating", adding: "It is a serious blow for fans who have been through so much and rely on football as a method of supporting themselves mentally with some normality and release.
"We should start the winter break now, and rearrange these matches when all fans have a chance to attend at a later date when hopefully restrictions are eased.
"During that time, we put our facilities and platform at the disposal of the local health authorities to ensure as many booster vaccinations can be administered as possible."
As well as limits on numbers, the first minister also confirmed one metre social distancing will be put in place.
A statement from the Scottish FA/Scottish Professional Football League Joint Response Group (JRG) did not make reference to any potential postponement of fixtures, instead saying they sympathise with clubs and supporters.
The statement also said the group are in discussion with the Scottish government to ensure any loss of income for clubs due to the new measures are compensated.
"Today's news will be a hammer blow to clubs and fans across the country, who simply could not have done more to mitigate the impact of the ongoing pandemic," SPFL chief executive Neil Doncaster said.
"Our clubs have adapted quickly and effectively to previous restrictions, and we will work with them in implementing the guidance from today's announcement in the coming days."
