The figures come as most of the remaining legal COVID restrictions in Scotland have come to an end.
Last week Nicola Sturgeon announced that laws requiring masks to be worn on public transport and in some other settings in Scotland will not be scrapped as planned due to the “current spike” in COVID cases.
Across the UK as a whole, 14,948 people with COVID were in hospital on 18 March, up 22% week-on-week.
This is still below the recent UK peak of 20,047 on 10 January and below the all-time UK peak of 39,255, which was reached during the second wave of the virus on 18 January last year.
Hospitalisations in southern England surge
The number of people in hospital with COVID in two regions of England has hit the highest level for more than a year.
South East England has now joined the South West in recording patient levels last seen in February 2021, surpassing the peaks reached in the previous surge of infections at the start of this year.
A total of 1,956 people with COVID were in hospital in the South East on 21 March, the highest since 19 February last year, according to NHS England figures.
In South West England 1,365 patients were recorded on 21 March, marking the highest since 9 February last year.
In both regions around half of people in hospital with the virus are being treated primarily for something else rather than COVID.
The total number of people in hospital with COVID-19 in England currently stands at 12,753, up 21% week-on-week and the highest since 1 February this year.
Infection levels rise across most of UK
Figures published on Friday by the Office for National Statistics (ONS) showed that infection levels are continuing to rise across most of the UK, with 3.3 million people estimated to have COVID in the week to 12 March, up from 2.6 million the previous week.
At the start of the year the figure stood at a record 4.3 million.