Nicola Sturgeon has urged shoppers to act responsibly and not to “squander” virus progress as more shops reopen.
Shops with outdoor entrances were reopening on Monday as part of phase two of lockdown easing, while indoor parts of shopping centres are expected to reopen on July 13.
Queues of shoppers formed at stores in Glasgow and Edinburgh ahead of doors opening on Monday morning.
The First Minister tweeted: “If you plan on visiting shops today, please do so responsibly.
“Maintain physical distancing, follow hygiene advice, wear a face covering and respect staff who may be asking you to shop differently.
“We’ve made so much progress against the virus – let’s not squander it. #StaySafe.”
Business minister Jamie Hepburn said police and health and safety officers could be used to enforce coronavirus guidance but shoppers have a duty to behave sensibly.
Speaking on the BBC’s Good Morning Scotland programme, Mr Hepburn said: “People should act responsibly and respectfully to other customers and to the staff so that minimises the need for enforcement measures.”
He added that people should only travel locally, shop alone where possible and wear face coverings unless health conditions would prevent it.
Shoppers could be seen queuing for shops to open, with hundreds of people gathering outside Primark stores in Glasgow and Edinburgh on Monday morning.
Queues in the capital ran along Princes Street, round into Fredrick Street.
Although police officers were present to watch the socially-distanced crowds gather to await the doors reopening, no trouble has been reported.
When Primark reopened at 8am, 10 shoppers were being let in at a time, with staff coming out to talk to people in the queue about what to expect.
Ahead of stores reopening, the Scottish Retail Consortium (SRC) trade body, along with trade union Usdaw and the Scottish Government, were encouraging people to follow five steps for “considerate shopping”.
They are: to queue considerately, maintain social distancing, follow instructions inside and outside shops, follow hygiene measures and be respectful to staff.
Earlier, First Minister Nicola Sturgeon said shopping trips would be “a bit different” from before the lockdown.
She urged people to treat shop staff with respect and follow their instructions.
David Lonsdale, director of the SRC, said: “Retailers have been working around the clock to create a safe shopping environment, so their customers can have the confidence to return to their favourite shops.
“Our shopping experience may be changing, but if we all follow the necessary social distancing and hygiene measures and show consideration to those around us, then everyone will be better off.”
The Usdaw union, which represents shop workers, said staff have a right to work without fear of abuse.
Stewart Forrest, divisional officer at the union, said: “Unfortunately the early part of the coronavirus crisis saw a rise in instances of abuse towards shop workers, and we are absolutely clear that ‘abuse is not part of the job’.
“Along with the SRC and Scottish Government, we have collaborated to produce guidance for shops of all sizes and locations to provide staff and customers with a safe shopping experience.
“Customers need to play their part and be patient, observe social distancing and show respect to shop workers, whilst ensuring high streets and town centres remain vibrant and a great shopping experience for everyone.”