Visiting will continue in Perth Prison and Castle Huntly.
Should prisoners show any symptoms of coronavirus, they will be forced to self-isolate within their cells.
The Scottish Prison Service (SPS) said it is planning for ways to allow self-isolating prisoners to maintain communication with their loved ones.
A spokeswoman said: “SPS is following the advice of Health Protection Scotland and we have issued guidance to staff and those in our care about steps which should be taken to prevent the spread of Covid-19.
“At this time there are no restrictions on movement in place, therefore establishments are continuing to operate visits as normal.
“Anyone within our care who is presenting with symptoms of Covid-19 is required to self-isolate within their cell for seven days.
“Those who are self-isolating still have access to food and medication and we are working on ways to maintain communication with friends and family.”