It is believed to be the first week no such action has been taken since lockdown restrictions were introduced nearly four months ago.
This includes against people flouting the mandatory wearing of face coverings in shops and on public transport.
They have been compulsory in shops since last Friday and on transport such as buses, trains, taxis and ferries since 22 June.
It is understood British Transport Police (BTP) has issued no fines for non-compliance on trains in Scotland, although there have been 21 fines on other parts of the rail network up to 8 July.
The latest Police Scotland figures, for the seven days to Wednesday, showed total fines issued, such as for illegal gatherings, was unchanged at 3,309 on the previous week.
The arrests total remained at 268, along with the 349 cases where people had been dispersed using “reasonable force”.
However, the number of people asked to disperse increased by 288 to 46,589 compared to the previous week.
Incidents where people were instructed to disperse increased by 106 to 11,036.
Police Scotland said: “We won't be providing a comment.”
BTP said across Britain between 29 June and 8 July, officers had spoken to 18,437 people on the rail network over not wearing a face covering, directed 817 to leave trains and issued 21 fines.
It said there had been a 97 per cent compliance rate across the rail network.
A BTP spokesperson said: "Our approach is to always begin by engaging with the public and explain the reasons why the protections are necessary and a lawful requirement.
"Since face coverings became mandatory on public transport, our officers have spoken with thousands of passengers, encouraging them to wear face coverings whilst travelling.
"The overwhelming majority of people have listened, complied, and continued to play an important role in protecting other passengers and rail staff.
"In those cases where people have refused to comply with the requirement, and they don’t have a valid exemption, officers have taken action by refusing entry to trains, directing passengers to leave services, and ultimately issuing fixed penalty notices and in some cases making arrests."
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