The latest weekly sampling by the Office for National Statistics suggest 473,800 people in Scotland had the virus in the week ending 20 March.
It came in the same week Covid patients in hospitals reached a record high.
And NHS Lanarkshire warned its three acute hospitals – Hairmyres, Wishaw and Monklands – were beyond full.
Medics said they were regularly running with capacity over 100% and they urged people to attend its accident and emergency departments only if their condition was urgent or life-threatening.
The surge in case numbers has been attributed to a more infectious Omicron sub-variant, BA.2.
The one in 11 rate was the UK’s highest, with England and Wales reporting one in 16 and one in 17 in Northern Ireland.
The number of cases in Scotland has risen from 376,300 last week – when one in 14 had the virus – to 473,800 people in this week’s data.
Meanwhile, there were 2,326 hospital patients with the virus on Friday – the fifth day in a row that Covid patient numbers hit a record high.
There were 10,100 new cases reported, with 41 new reported deaths of people who have tested positive.
Official figures also showed there 28 people in intensive care with recently-confirmed Covid-19 in the past 24 hours.
A total of 4,341,965 people have received their first dose of a vaccine, 4,089,894 have had their second dose, and 3,446,630 have received a third dose or booster.
Despite the sharp rise in patients in hospital with Covid, fewer of them are requiring intensive care treatment than in the past.
This is partly because Omicron is believed to be milder than previous strains such as Delta, most people have been vaccinated and doctors have better treatments for the disease.
However, people with Covid still need to be kept separate from other patients to limit the spread of infection – something that puts pressure on ward capacity. It is also leading to increased staff absences.
Hospitals ‘beyond full’
NHS Lanarkshire said the number of Covid patients was putting pressure on services at University Hospital Wishaw, University Hospital Hairmyres in East Kilbride and at University Hospital Monklands in Airdrie.
Dr Jane Burns, executive medical director, said many were patients waiting several hours to be seen in emergency departments, and urged people to consider whether A&E is the best place for them to seek healthcare.
“Our three acute hospital sites are beyond full with capacity regularly over 100%,” she added.
“This has been the case for a number of weeks and the situation is not easing. In fact, this week hospitals across Scotland including Lanarkshire have seen a record number of Covid patients.
“Unfortunately, this is resulting in many patients in our emergency departments waiting well in excess of our target of four hours for a condition that could have been treated by another healthcare service. It is also putting pressure on how quickly we can admit patients who require emergency care.
“The rising Covid number is also having a severe knock-on effect to our staff. We have high staff absences due to Covid and self-isolation which is resulting in challenges across all our health services and our staff are struggling to cope.”
She urged people to think of alternatives to the emergency department if their condition is not critical or life-threatening.
Other services include minor injuries units, their local GP or pharmacy or a call to NHS 24 on 111, day or night.
She added: “If someone does have to come to one of our emergency departments, they need to be prepared to face long waits to be seen, in some instances several hours.”
It comes after NHS Greater Glasgow and Clyde this week urged people not to attend accident and emergency departments unless their condition is “urgent or life-threatening” amid significant pressures.
Having visited a number of hospitals recently, the national clinical director Prof Jason Leitch told BBC Radio Scotland’s Drivetime programme that the NHS was under the most pressure he had ever seen.
He said people should “do what we can as a population” to reduce the pressure on the NHS – but urged them to use emergency services if needed.
He added: “We don’t want people not to come if they need it – what Glasgow and Lanarkshire are asking is just use it wisely.
“Use NHS24, your GP, your dentist, your optician – don’t just use A&E as your one stop shop. But if you have an emergency, 999 is available to you and you should use it if you need it.”
Latest official figures this week showed that the number of people waiting more than four, eight and 12 hours at Scotland’s emergency departments has hit its highest recorded level.
Commenting on the figures, the Scottish government said: “Unfortunately, the number of people in hospital with Covid-19 has now reached the highest level since the start of the pandemic and this rise in recent weeks has inevitably had an impact on services like A&E.”
