NHS Tayside said it is investigating a “small number” of cases in wards two, three and 19.
The health board said tests have been offered to patients in the wards and relevant staff.
A spokesman said: “The wards are not accepting new admissions and visiting has been temporarily suspended.
“All appropriate infection prevention and control measures have been put in place and Public Health Scotland has been informed.
“The public should be reassured that NHS Tayside has separate care pathways for patients presenting with Covid-19 symptoms, for urgent presentations and for patients attending for planned procedures or treatments. These pathways are supported by testing for Covid-19.”
He added the health board tests asymptomatic workers in line with Government guidance and provides appropriate personal protective equipment for staff working in areas with confirmed or suspected coronavirus patients.