Inmates will not have access to courts, lawyers, family visits and cannot use the gym, but will be allowed fresh air and showers as well as use of mobile phones, the SPS added.
The service said a “significant number” of affected prisoners did not have symptoms.
HMP Perth holds an average of 678 prisoners per day, including prisoners serving life sentences and sex criminals, said the SPS.
A spokesman said a “significant number” of the positive cases at HMP Perth were asymptomatic.
“As a precautionary measure, all individuals living in HMP Perth are currently isolating whilst mass testing is carried out.”
A further update will be provided on Monday, the spokesman added.