Pubs and cafes have been warned they could be shut down after a number of breaches were raised with Nicola Sturgeon.
The First Minister told hospitality businesses they "cannot allow standards to slip" - and told members of the public to avoid premises failing to follow the rules.
At her regular coronavirus briefing, Sturgeon said: "If we do start to see outbreaks linked to the hospitality sector, we would need to take action, and that could include closing premises down again. Nobody wants to see that happen.
Sturgeon added: "So I want to send a message to everyone in the sector today that these guidelines aren't just for the first few weeks. They must become the norm, and you cannot allow standards to slip.
"And, to customers, if any venue you are visiting or frequenting doesn't seem to be taking Covid seriously - for example, if you're not asked for your contact details, if there's not clear guidance in place about physical distancing, my advice to you is go somewhere else."
Hospitality was allowed to get back to business with outdoor seating three weeks ago and indoor serving two weeks ago.
A new Scottish Government document has been produced for the hospitality industry to ensure they are fully aware of what their responsibilities are.
Sturgeon earlier praised efforts across hospitality premises to make major changes to accommodate the new reality of coronavirus.
She said: "There's been a lot of hard work by businesses and staff across the country to make their premises safe for visitors, however although the majority of businesses are following the rules, we do know anecdotally of some instances of guidance being breached, of seating areas not being cleaned thoroughly between customers, of staff not wearing face coverings, and of contact details for test and protect not being taken."
