Chief constable Iain Livingstone admitted he never expected see the force have such "extraordinary" controls which could see the public hit with spot fines and even arrested if they breach strict new lockdown rules.
The powers have already proved controversial south of the border where police have used drones to track down dog walkers and unveiled plans for checkpoints.
But Mr Livingstone told BBC Radio Scotland's Good Morning Scotland today: "I would ask for the public's forbearance at this time. Our officers will always act in a reasonable manner, a fair manner, in a proportionate manner.
"A lot of this will be done through engagement, through communication, through a level of discussion and to be brutally frank there needs to be a lot of common sense applied.
"This is an extraordinary time, the key issue is for people to continue to comply with the guidance that's issued not because you can end up having a fixed penalty or because you can end up having an engagement with the police service. The reason to do id to protect your fellow citizen, the reason to do it is to protect the health service, the reason to do is so that everybody's safe."
It will mean police have powers to disperse gatherings of two or more people outside, as well as ordering people home if they are found to be outside without good reason. This could include shopping, getting medicine or one daily form of exercise a day.
Fixed penalty notices of £30, rising to £60 if not paid within 28 days. These penalties are doubled for each repeat offence up to a £960 cap, with no reduction for early payment. The regulations will be reviewed at least every 21 days to ensure they are still necessary.
Nicola Sturgeon has also warned that in some cases Scots could be prosecuted.
"They are undoubtedly extraordinary powers and they're extraordinary powers because we face an extraordinary threat,” Mr Livingstone added.
"They have a level of enforcement given to the police service in Scotland that I certainly never envisaged but they are there because of the criticality of the threat facing us."
It will mean that police now have the powers to order the lockdown of pubs, clubs, gyms and restaurants and enforce “social distancing” measures in food retailers like supermarkets which remains open.
The police chief praised the approach of the public so far less than a week into the lockdown.
"There's enormous reorientation for every citizen, for businesses - all groups, not least the police service ourselves - to get used to this set of circumstances," he said.
"Compliance levels thus far have been fantastic."
But he added: "There will unfortunately at times be a number of individuals who for whatever reason will not comply and therefore I do welcome the fact that there is now a lawful framework to enforce these guidelines if they are needed."
Police Scotland now have the power to to enforce restrictions on movement of people outside their homes and to disperse gatherings. This means officers can remove people who are outside their home without a “reasonable excuse” if the police officer has reason to believe it is a “necessary and proportionate” approach.
The Scottish Government’s Constitution Secretary Michael Russell said: “There has been a huge effort by the people and businesses of Scotland to respond to the unprecedented situation we face dealing with the coronavirus.
“I would like to thank everyone who is playing their part by staying at home to ensure the social distancing measures we have introduced help stop the spread of the virus.
“While the majority of people are doing the right thing, these regulations provide the police with emergency powers to enforce social distancing where necessary.
“It is only because of the unprecedented crisis we are facing, and to save lives, that these powers are being introduced. They are temporary and will be kept under review.
“I urge the people of Scotland to continue their outstanding collective effort and follow the rules that have been laid down.”