Jeane Freeman, speaking on BBC Breakfast on Sunday, said the Scottish Government will have an announcement "very shortly" on any more restrictions.
It comes after there was a rise of 350 positive Covid-19 cases in Scotland on Saturday - the highest daily increase in four months.
The rate of transmission in Scotland - or R-number - is now believed to be between 1.1 and 1.4.
First Minister Nicola Sturgeon warned on Friday that greater measures may have to be put in place "if we want to avoid another full-scale lockdown".
Ms Freeman said on Sunday: "We're not seeing community transmission at this point, but are seeing large clusters and outbreaks of cases in some parts of Scotland.
"So we're working this weekend with scientific and clinical advisers to understand what might be the additional measures that we can put in place."
She added that Ms Sturgeon had hoped to have a Cobra meeting with the four nations this weekend to discuss measures "to see if we could reach a shared view", but that the Prime Minister was still considering the request.
When asked when the decision on lockdown measures may be made, Ms Freeman replied: "We certainly will have an announcement very shortly. Not necessarily today, but definitely by the early part of next week."
Ms Freeman also said she did not believe Scotland would move to the large fine route that England had taken.
In Scotland, police have the ability to issue fixed penalty notices of £30, rising to £60, for those who break restrictions.
‘Mixing households risk’
Ms Freeman’s comments were followed by remarks from National Clinical Director, Jason Leith, who said the Scottish Government is looking at ways to reduce households meeting up.
He said in a radio interview today: “The main risk is mixing households. So if you think about that and you were the public health adviser to the First Minister, what kind of things would you try and restrict?”
"So that takes you into the territory of trying to stop people meeting in houses and trying to stop people meeting across households in areas like hospitality because that's the biggest risk, that's where the virus spreads, and that's where people get sick.”
Mr Leitch added: “I don't think we're heading into full lockdown like March the 23rd, but we're certainly looking at trying to reduce households meeting up. And that's where the virus likes to jump from household to household.”
Ms Freeman said: "Isolating for 14 days is a serious request in terms of people's financial situation.
"We also need to understand very many people are in low-paid jobs, with fragile contracts, sometimes in really difficult circumstances, so we need to win people to this fight with us.
"Simply imposing fines if they don't won't be sufficient.
"Those are big numbers, which for many people will be completely beyond their capabilities."
Scottish Labour leader Richard Leonard warned lessons needed to be learned from the first nationwide lockdown, saying: "I understand that the decision on further restrictions will not be made lightly but it is vital that we know the plans that are in place to ensure the failings at the start of lockdown in March are not repeated.
"Nicola Sturgeon has said time and again that with the benefit of hindsight she would have made different decisions regarding care homes.
"Lessons must be learnt so that the devastating impact on care home residents and staff does not happen again.
"We need to know that the right PPE is in place and that supplies won't run out, that the testing regime is fit for purpose and that transfers from hospitals simply do not happen unless it is absolutely confirmed the person is Covid-free."