The legal restriction on travelling between areas in level three or four of Scottish Government coronavirus regulations, as well as outside the country, came into effect on November 20.
The move was described as being unenforceable at the time, with the chief constable assuring Scots there will be no random vehicle stoppages or road blocks.
Questioned on the issue at First Minister's Questions at Holyrood on Thursday, Nicola Sturgeon confirmed Police Scotland handed out 33 fines in the first five days of the travel ban.
SNP MSP Stuart McMillan told the First Minister he had heard reports from his constituents in Inverclyde, which is under level three restrictions, of people travelling into the area to shop, and he asked her whether more support can be given to police on the ground to uphold the new law.
She said: "It remains vitally important that members of the public continue to observe physical distancing, wear face coverings and avoid non-essential travel into or from level three or level four areas.
"The need to restrict travel across the country is even more important now in the battle to reduce transmission rates because we don't want to take the virus from high to low prevalence areas.
"The purpose of all of these restrictions, which none of us enjoy living under, is to protect the NHS and save lives by preventing the virus from spreading."
Ms Sturgeon said policing resources are a matter for the chief constable, but she added she is sure officers will continue to deal with the coronavirus laws "appropriately".
She said the Scottish Government and Police Scotland rely on "high levels" of compliance from the public.
Ms Sturgeon told the chamber: "We want to see these laws work through high levels of public compliance rather than relying on enforcement.
"That said, Police Scotland will uphold the law using the same approach they have adopted since the start of the pandemic."
Scotland’s travel ban has meant it is effectively illegal to travel to the airport or to a port to travel abroad, but taking the flight itself is still legal.