Speaking at the Economy, Energy and Fair Work Committee at Holyrood, Ms Hyslop was asked by Labour MSP Jackie Baillie about companies remaining open despite calls from the UK Government to close.
Ms Baillie pointed to the particular example of Sports Direct after parent company Frasers Group reportedly claimed the retailer was a vital service.
It bowed to public pressure and closed on Tuesday.
Ms Hyslop said how businesses act during the pandemic could cause reputational damage.
She said: "I think the public will take a very poor view of people who are deliberately compromising the public health now.
"I think the reputations of a number of companies who are forcing their workforce to come in will be irreversibly damaged.
"Therefore they themselves need to think about that."
The Economy Secretary said emergency powers legislation due to be passed before the end of the month at Westminster will help to force non-essential businesses to close.
Police Scotland have said they "will not hesitate" to use the new powers to protect public health including giving officers the ability to issue emergency closure orders.
The Economy Secretary said: "The police, who at a time of a public health crisis have better things to do as part of planning and support of health services, had to resort to emergency provisions on licensing.
"Now, licensing, because it's the sale of alcohol, is easier to close but that's what they had to do.
"I think that it's really not the proper use of their time but they had to do that.
"I've got great admiration for those companies that have taken it seriously, had their business continuity plans, thought through what they would do and then executed it very quickly.
"But there are some exceptions and unfortunately it's not just themselves that are affected."
She added: "The way that this has been approached in Scotland has been to try to be transparent with people, to take people with us so that everybody can work together on this, because if you feel you're part of a national mission to do this, then I think people will go the extra mile."
MSPs will vote on giving the consent of the Scottish Parliament to the emergency UK Government legislation on coronavirus on Tuesday, with the motion expected to pass