Professor Leitch said rising cases may mean a “reverse gear” on restrictions was required, but did not specify in what areas controls could be put in place.
Scottish Hospitality Group (SHG) spokesman Stephen Montgomery said there could be a major collapse of hospitality venues by the end of the year, especially if further lockdowns are implemented.
He said: "It’s all very cloak and dagger – what are these sectors of society? It is a major worry.
"You can’t come out and make a comment like that and not back it up, especially after the 18 months we have just been through. It feels like they’re just saying ‘it could be you’.
"If there is anything we have learned from the pandemic, it is that last-minute decisions don’t work. We are not a light switch, which can be switched on and off again easily. Everything takes planning.
"Hospitality is always the first to go and the last to come back, we know that. A lot of hospitality businesses are just now treading water and furlough is keeping them afloat.
"Come Christmas, I think we are going to see a lot of businesses going to the wall and any further lockdowns could be a disaster for the industry.”
Mr Montgomery said the SHG had a weekly call with Scottish Government officials, who had given the industry no hint of further shutdowns.
He said: "There have been no discussions with the government. We have asked them every Wednesday for the past six or seven weeks ‘what we are going to do if cases rise and nothing?’. There was no suggestion last Wednesday that this was on the cards.”
Prof Leitch’s comments come as the rolling weekly total of coronavirus cases rose to 37,968 – the highest ever recorded.
The figure is up by almost 80 per cent compared to the week before.
There were 3,393 new cases of coronavirus recorded in the 24 hours to Monday, compared to fewer than 1,500 on August 9, when most of the Covid restrictions in Scotland were lifted. However, on Sunday, the Scottish Government reported more than 7,000 cases in a daily first.
Speaking in a BBC interview, Prof Leitch warned that there had to be a "reverse gear" to protect public health, but said further restrictions might not be a "short, sharp shock", but turning off "some bits of society".
He said: "Reverse might look a little bit like forward gear going backwards, if you’ll forgive me for saying so, rather than a short sharp shock. It might be that you’d have to turn off some bits of society. I hope we don’t have to do any of that, which is why vaccination, testing, self-isolate if you’re asked to and follow the rules.”
He added that it was harder to “turn off” parts of the NHS than other sectors.
The number of hospital patients rose to a total of 551 on Monday, with 52 in intensive care.
"The only thing you can turn off in a health system is elective care,” Prof Leitch said. “You can't postpone strokes, heart attacks and emergency admissions for the elderly.
"We don't want to do that, but if you need staff, beds etc for a novel infection disease then that's what you have to do because you can't just make respiratory consultants out of nowhere, or nurses in charge of intensive care out of nowhere, so you have to be flexible in that."
NHS Lanarkshire and NHS Glasgow rank top of the worst-hit regions in Europe with case rates of 853 and 748.5 per 100,000 people respectively, based on World Health Organisation (WHO) figures.
There are a further six Scottish health boards in the top 20 – Lothian, Dumfries and Galloway, Forth Valley, Ayrshire and Arran, Highland and Fife.
Prof Leitch said the health service was under pressure already, "with or without Covid".
He said: "[We have] over 500 now in hospital and a doubling of the case rate every seven days, so we really want to get on top of it."
Overall, 82.1 per cent of over-18s in Scotland are fully vaccinated and 91.1 per cent have had at least a first dose, but Prof Leitch said he was working with those who were hesitant to get the vaccine.
“They have got legitimate questions," he said.
"Some of it is, of course, scientific nonsense. The fertility one – there is no biological method where a vaccine could hurt fertility in any conceivable way – but there are legitimate questions about the blood clots, about allergies, that we can answer. When we answer, people come forward [for a vaccine].”
Scottish Labour have criticised the government for letting Covid spiral out of control over the summer, saying the lack of resourcing for Test and Protect has put the system on the verge of collapse.
The party’s health and Covid recovery spokesperson Jackie Baillie also criticised the government for failing to convene the Parliamentary Covid Recovery Group.
She said: “Covid levels are spiralling out of control across Scotland as ministers come back from their summer off.
"Instead of learning the lessons from last year, the SNP have wasted the last two months, and now we are sending pupils back to unsafe schools and unvaccinated students off to university."
Ms Baillie said: “Test and Protect has been all, but abandoned and the vaccine roll-out has stalled – but the Covid Recovery Group didn’t have a single meeting. The SNP’s attitude has been nothing short of negligent – it is little wonder cases are at an all-time high.
“We need to see some real accountability when the new parliamentary term starts, so we can get the virus back under control and keep people safe.”
The Scottish Government said decisions on any further restrictions were a matter for Cabinet, but pointed out that the risk of Covid is higher indoors, in crowds and in poorly ventilated environments.
A total of 82.1 per cent of over-18s in Scotland are now fully vaccinated, while 91.1 per cent have had at least a first dose.
Almost all remaining restrictions were scrapped in Scotland on August 9, with all venues including nightclubs allowed to open. The government has, however, retained a requirement to wear masks in indoor spaces, apart from when eating, drinking or dancing in a nightclub.
The warning around a “reverse gear” on restrictions comes as NHS Lanarkshire announced patients would only be allowed one dedicated visitor per day due to rising Covid case numbers at hospitals across the health board.
Officials said the move would allow the NHS board to manage the environment and maintain physical distancing within multi-occupancy rooms and across communal areas.
Nurse director Trudi Marshall said: “We understand that patients in hospital are having a challenging time and want to have their family and friends around them for support.
“Unfortunately, we have seen a rise in the number of Covid patients in our hospitals, and it is our priority to protect our patients and staff as much as is possible. This is why we have made the difficult decision to have one dedicated visitor each day.
“The named person will be able to have close contact with their loved one, such as holding hands. This will provide those patients in hospital with the vital support they need from family, carers or friends.
“Visiting will continue to be by appointment only and visitors should contact the ward to arrange a time to visit.”