In a press conference after a call with other UK leaders, Ms Sturgeon said a planned relaxation of Covid-19 restrictions - allowing households from around the UK to mix indoors at Christmas - would be abandoned.
The last minute decision, prompted by a surge of cases of a new, more infectious strain of coronavirus in the southeast of England and Wales, also included a ban on Scots travelling to other parts of the UK.
Ms Sturgeon insisted that enforcing the ban was a “procedural matter” for Police Scotland.
But the force has now confirmed that it will not change its approach to policing travel, and would use enforcement only “as a last resort”.
In a statement following Ms Sturgeon’s briefing, Assistant Chief Constable Alan Speirs said: “I fully understand that people will be disappointed with the tightening of restrictions, particularly at this time of year.
“The vast majority of the public have been complying with the regulations and so the policing approach we adopted from the outset of the pandemic will not change.
“Our officers will continue to engage with the public, explain the legislation and guidance, and encourage compliance. We will use enforcement as a last resort where there is a clear breach of the legislation.
“The Chief Constable has called on people to take personal responsibility to do the right thing and remember the purpose of these measures is to aid the collective effort to save lives by preventing the virus from spreading.”
"We have been very clear that we will not be routinely stopping vehicles or setting up roadblocks.
“However, officers may in the course of their duties come across people who are travelling from one local authority area to another.
“Where travel restrictions apply, officers will continue to use the common sense, discretion and excellent judgement that they have applied since the crisis began."
It comes as Prime Minister Boris Johnson announced that from Sunday areas in the South East currently in Tier 3 will be moved into a new Tier 4 – effectively returning to the lockdown rules of November.