Nicola Sturgeon has not ruled out bringing in even tougher lockdown rules despite the country already being ordered to stay at home.
The First Minister suggested non-essential businesses could face further curbs in a bid to prevent people from meeting each other and passing on coronavirus.
Mainland Scotland was placed in lockdown as of Tuesday, with people told to remain indoors unless venturing out for one of several essential reasons.
Schools are also shut to the vast majority of pupils and will not reopen until February at the latest.
But despite the measures, the SNP leader said in an interview with Good Morning Britain that further restrictions could be required.
She said: "If people abide by them, I hope and believe we can see the case rise stem and hopefully cases start to decline but I'm not complacent about that yet, we are monitoring traffic numbers for example to see the extent to which this lockdown is keeping people at home.
"There is a question in my mind about whether we need to go a bit further in restricting non-essential business activities to cut even further the reasons that people have for being outside of their own home and that's something I will be looking at with my advisers over the next few days."
The First Minister repeated her hopes that over 900,000 doses of coronavirus vaccines will be delivered to Scotland by the end of the month.
The Scottish Government plans to vaccinate up to one million Scots by the end of January, however Sturgeon said vaccinations are dependent on supplies.
The First Minister is expected to discuss the possibility of further lockdown measures at her daily media briefing at 12.15pm.
