Dr Lewis Morrison, chair of BMA Scotland, said the NHS was facing a “double whammy” of winter pressures and the latest coronavirus variant.
On Friday, Nicola Sturgeon announced Omicron was now the dominant strain of the virus and a “tsunami” was beginning to hit Scotland.
Speaking to the BBC’s Good Morning Scotland programme, Dr Morrison said: “For this to coincide with the usual pressures, which are generally due to people being sick, they’re not the routine work, at this time of year it’s a bit of a double whammy.
“People are really tired now.”
Asked about medical staff being required to self-isolate and the pressure this was putting on medical care, he said: “I think if we see a huge number of cases of the new variant it’s highly likely to impact the medical workforce.
“From a hospital perspective, it’s the effect it may have on nursing staff particularly because it’s nurses that keep the wards safe at the most basic level.
“Although we can to some extent redeploy staff, there are real limits on how much we can do that.
“It remains to be seen what proportion of the NHS workforce might end up self-isolating either temporarily or for longer, but that’s got to be a huge worry.”
Virus expert Dr Christine Tait-Burkard, of Edinburgh University, told the radio programme that the symptoms of Omicron had changed compared to the Delta variant and often resembled the common cold, while the virus seemed to last for shorter periods in infected people.
Omicron was very good at spreading in large, close-contact settings such as nightclubs, she said.
Dr Tait-Burkard said: “We have seen Wales closing down nightclubs after Christmas, it is a good potential that that might happen in Scotland as well alongside large events.”
Discussing suggestions the latest wave of cases could rise and fall quickly, she said: “It’s going up with such lightning speed that eventually the virus runs out of people to infect for multiple reasons.”
This could still lead to a large number of people ending up in hospital in a short timeframe, she said.
The UK Government is due to hold a Cobra meeting this weekend as devolved administrations demand more money for their measures to tackle Omicron.
A phone call involving Nicola Sturgeon and Boris Johnson also took place on Friday.
A spokesperson for the First Minister said she emphasised the “extreme urgency of the crisis” for businesses.