Mr Yousaf said the Scottish Government needs to “balance” the various harms” that could result from tougher restrictions.
He warned that even the “best case scenario could be extremely challenging” for the NHS this winter.
He told BBC Radio Scotland’s Good Morning Scotland programme that following the arrival of the Omicron strain of coronavirus in Scotland, there had been a “really worrying rise in cases”.
He said Omicron infections had made up about 6% of all Covid cases a week ago but that has now risen to “about 36.5%”.
Mr Yousaf said: “This variant is the fastest, most transmissible variant we have seen during the pandemic.
“Even the best case scenario could be extremely challenging if we don’t take measures to protect ourselves, that’s why the First Minister made her announcement on Tuesday, asking people to minimise their social contacts as best they can, given the high transmissibility of the virus.”
Nicola Sturgeon has urged people to reduce their social contacts over the Christmas period, limiting gatherings to three households or fewer.
Shops and other businesses are being told to introduce further measures to help prevent the spread of the virus.
But Mr Yousaf dismissed the idea of a circuit-breaker lockdown, saying: “We have to always balance the harms, that is why we haven’t imposed more restrictions perhaps than we are doing at the moment, because we understand 20 months into this people’s mental health is suffering, the economy is suffering, people’s wellbeing is suffering, there has been educational disruptions.
“Of course as a Government there are other measures we could take that could limit social mixing, but they would come at harm and at a cost.
“The Government’s job is to balance those various harms and I think that is the balance we have got right.”
He also said work is being done “at pace” to discharge people from hospital if they are well enough, saying there are currently about 1,500 patients on wards who are “safe to be discharged”.
He said discussions with Edinburgh City Council had revealed that 28 people in the area are refusing to be discharged from hospital despite it being “clinically safe” and there being a care home space waiting for them, and the Health Secretary appealed to the public to “help us with this”.
He also again urged all those eligible for a booster to get vaccinated, saying: “Get that booster, it can protect you, it can protect your family and it can also help us with the pressures we are facing with the NHS.”
He insisted ministers are “doing everything we possibly can” to hit the target of having 80% of eligible adults boosted by the end of the year, with the remaining injections to be completed shortly after this.
Health boards are considering extending opening hours for vaccine clinics, Mr Yousaf said, though he added jabs will not be given on Christmas Day or Boxing Day.
“We’re making good progress in Scotland, but I need us and I want us and I will ensure we go even faster than we’re going at the moment.”