Some 2,969 cases were recorded – an increase of more than 200 on the next highest daily total in early January.
Test positivity was 7.3 per cent, with a record 42,310 tests taking place.
The results came as 13 deaths with Covid-19 on the death certificate were recorded in the week to June 20, bringing the weekly count to double figures for the first time since April.
First Minister Nicola Sturgeon urged people to take the high case numbers seriously and follow restrictions until they are lifted in July and August.
Professor Devi Sridhar, chair of global public health at Edinburgh University, also urged caution, but warned against “unhelpful panic” around the figures.
Some have blamed the increase in cases on football fans mixing during the European Championships, as cases have risen particularly in young men.
Case numbers in men aged 20 to 24 this week have been three times those in women of the same age – 765 and 240 respectively.
In the 25 to 44 age group, there have been twice as many infections in men – 918 compared to 426
The gender split is more even in younger and older age groups.
Linda Bauld, professor of public health at Edinburgh University, said the high case numbers were due to three factors: people following restrictions less, especially around social distancing; the Delta variant, which is more transmissable; and a sudden increase in cases among young men, the cause of which she declined to speculate about.
“Throughout the pandemic we’ve had a pretty equal relationship between male and female cases, and in fact at some points we had more women testing positive, for example health and care workers, because proportionately more of them – particularly care workers – are female,” she said, adding the current higher numbers of cases in men is “really weird”.
However, the discrepancy is likely to be short-lived, she said, as men will pass the virus to the rest of their household.
“What happens is, of course, it passes around the household, so we have more men now for a few days, which is really weird, but that will even out because they will pass it on to their wives, girlfriends and female children,” she said.
Prof Bauld did not pinpoint football as a cause of the increase in cases, but said: “We know from multiple behavioural studies that young men are more likely to take risks.
“So they will will be more likely to engage in more interactions that are outwith what the guidance recommends, so clearly that is happening.”
Prof Stephen Reicher, a behavioural psychology expert at St Andrews University who advises both the Scottish and UK governments, said football was the “obvious explanation” for the discrepancy.
He told the BBC's Good Morning Scotland programme on Wednesday: "A few weeks ago it was about 50:50, men and women got infected at the same rate. Yesterday the data showed that young men – men under 45 were about three times more likely to get infected.
"We can't be sure why that is, but the obvious explanation is that people were getting together for the football and not taking precautions."
National clinical director Prof Jason Leitch said he did not think football was to blame, but that among young men the virus has been spread mainly by indoor socialising.
He told BBC Radio Scotland's Drivetime with John Beattie on Wednesday that dates for further easing are dependent on people following restrictions, and could be delayed if Covid figures got out of control.
Ms Sturgeon wrote on Twitter: “Another big increase in Covid cases in today.
“First, some context: a record number of tests were done yesterday, and % positive is down a bit.
“But…if we want to get to end of restrictions on August 9 safely, we should take this increase seriously.”
Vaccines are breaking the link between cases, illness and death, she said, but a “sizeable” percentage of the population is still unvaccinated.
Just over 40 per cent of adults in Scotland are yet to receive both doses of vaccine.
The First Minister has said that all over-18s should receive a first dose by July 18, and two doses by September 12.
"Most cases are now in younger, yet to be vaccinated groups, so fewer are becoming very ill,” Ms Sturgeon said.
Around 5 per cent of cases are admitted to hospital now, she said, half the rate in January.
But she added 5 per cent of a large number of cases will still “put huge pressure on NHS and cause suffering and loss”.
"We are much more confident about the medium term (ie from Aug 9), due to vaccines, but what we do in short term will determine how safely we get there,” she posted.
"So – even tho we’re all fed up & frustrated if we see others breaking rules – it’s still important to take this seriously.”
Prof Sridhar tweeted: “Seeing lots of unhelpful panic over today’s numbers. Obviously caution needed, but most important marker is whether link between cases and moderate to severe disease being broken.
"This is a different wave than previous ones. We are in new territory.”
Prof Sridhar added that she was “very concerned” about South Asia, Latin America and Sub-Saharan Africa at the moment, where there are not enough vaccines, not enough oxygen and hospital beds, and no economic support for people to stay at home.