Organisers said the “majority” of its programme was expected to be affected by restrictions, with some shows cancelled completely.
However final decisions on this year’s festival will not be taken until after a crucial announcement from the Scottish Government on the possible easing of restrictions next week.
An official statement said the event was “committed to presenting a form of the festival which brings the connection and joy of Celtic Connections to audiences, while being both feasible and safe for all involved.”
The festival, which is in its 29th year, was thrown into chaos before Christmas after the Scottish Government announced that strict curbs on live events would be in place until 17 January – three days before the opening concert.
Under the current restrictions, audience numbers for indoor events are capped at just 200 for all-seater shows and 100 for standing gigs, with all venues having to enforce one-metre distancing.
In an initial statement before Christmas, Celtic Connections said the government’s measures and the timeline for future reviews presented “significant challenges.
It is thought the festival is trying to salvage as many shows as possible which could go ahead in some form, including online broadcasts.
First Minister Nicola Sturgeon offered hope to event organisers on Tuesday when she said she was “very” hopeful that the current restrictions would not be needed beyond 17 January.
However it is unclear what measures, such as physical distancing capacity limits, will have to be kept in place.
Ms Sturgeon also told MSPs that work was underway on a new “framework” of restrictions to manage Covid which will be “more proportionate, sustainable and less restrictive.” However Ms Sturgeon would only say that it is due to be published “over the next few weeks.”
A spokeswoman for the festival said: “It is with a heavy heart that we confirm a number of shows and elements within the programme are no longer able to go ahead.
"We’re in the process of contacting impacted artists regarding cancellations and expect the majority of shows to be affected by restrictions in some way.
“Our ambition for the 29th edition of the festival was to bring everyone together once again.
"However the uncertainty and disruption caused by the Omicron variant has meant it’s not feasible for us to continue with our existing plans on the scale we[d originally hoped.
“Artists and ticketholders for shows affected so far are being contacted directly and we would like to thank everyone for their ongoing support and patience.
“We’re also encouraging all artists impacted to apply to the Creative Scotland COVID-19 Cancellation Fund for Creative Freelancers to help with financial support during this difficult and uncertain time.
“We’ve not come to these decisions lightly and are committed to presenting a form of the festival which brings the connection and joy of Celtic Connections to audiences, while being both feasible and safe for all involved.
“We’re currently working through many different scenarios and options and reviewing all shows in line with existing event restrictions. We’ll continue to keep our audiences up to date as the plans for Celtic Connections 2022 evolve.”