It is the third time in a week the record for new infections has been broken, with more than 7,000 in fections recorded for the first time.
The health secretary also warned people not to call 999 unless it is “absolutely critical” as the ambulance service and accident and emergency strain under the pressure of Covid-19.
New cases have more than doubled in a week, although today’s figure includes some tests taken more than 48 hours ago due to backlog and delays in the testing system.
Mr Yousaf said: "What you are seeing in many local health board areas is that the A&E departments are almost at pre-Covid levels - and in some areas, above pre-Covid levels.
"Add to that, just shy of 500 Covid patients across the country. And, of course, we've still got infection prevention control measures in place.
"We've also had staff absence through illness and some taking annual leave, understandably.
"All of that is a real perfect storm putting enormous pressure on our health service."
Mr Yousaf said that it was vital Scots only called 999 if it is “absolutely critical” as he defended the straining accident and emergency departments across Scotland.
He said: "The NHS is absolutely and utterly interconnected. If you are having problems within the A&E department, that's a whole-systems problem, so the demand on the ambulance service is huge.
"But, of course, if the ambulance gets to a hospital which is under severe pressure, then discharging someone from an ambulance and getting them seen also takes time.
"That then affects the ambulance going back out to recover another patient.
"So that's why we're asking people, only to call 999 and only request an ambulance if it is absolutely critical."
Meanwhile a leading public health expert said while rising Covid cases in Scotland are “concerning”, renewed restrictions or a circuit breaker lockdown is “unlikely”.
Linda Bauld, professor of public health at the University of Edinburgh, said it was possible Scotland could see 14,000 positive cases a day.
In July, Mr Yousaf said the Scottish Government “wouldn’t want to tolerate” around 8,200 cases per day when asked about the UK Government’s advice that the country could see 100,000 cases UK-wide after ‘Freedom Day’.
At the time, Mr Yousaf said such high case numbers would still cause “pressure” on NHS Scotland.
Speaking on BBC Radio Scotland’s the Sunday Show, Professor Bauld said the figures were concerning and predictions of it reaching 14,000 in a day would be worrying.
She said: “That is a doubling rate of about a week and we have seen a doubling in a week of the number of cases and it is not just that we are doing more testing, test positivity is up.
"The problem is that the interactions that are occurring now, and again you can see from that same analysis that people have more contacts, amongst people in their 30s the biggest change is many more of them back in the office or at work, that’s a real shift over the last week or two.
"If that continues, because you have seeded more infection in a community, particularly some parts of Scotland, it is going to to take a while for it to settle down, so it’s definitely not impossible.”
In total, 52 people are in intensive care with Covid-19, while a further 507 are in hospital.
A total of 4,101,311 people have now received a first dose of Covid-19, with 3,655,287 having received a second dose of the jab.
No deaths were recorded on Saturday.
Asked whether restrictions were likely to be reintroduced, Professor Bauld said she did not see that as a likely outcome.
She said: "Many countries around the world promise their populations that if they came forward and took up vaccines, that would be alternative to having severe restrictions while still having to maintain things that are basic public health and the Scottish people have done that.
"For a government to say ‘oh well actually, we’re just going to go back to where we were in 2020 and shut things down again is difficult.
"I think things would have to get a lot worse in terms of hospital capacity for that to occur and I don’t see that on the immediate horizon despite there being some challenges in some areas."
Speaking on Twitter, Nicola Sturgeon said: “We are seeing a rising curve of cases in Scotland. It’s reassuring that vaccines are preventing the levels of serious health harms that case numbers like this would once have caused.
“However, we can’t be complacent and are monitoring carefully. In meantime, please take care.”