The Scottish Fire and Rescue Service extinguished each of the blazes in Prince Street, Erroll Street and Drummers Corner.
There were no reports of any injuries.
The fires are all being treated as wilful and enquiries are ongoing.
Detective constable Debbie Mitchell said: “Deliberately starting fires is reckless and can have extremely serious consequences.
“We are investigating these incidents and would urge anyone who may have information to get in touch.
“This includes anyone who may have dashcam footage or private CCTV from the area.”
If you have any information, call 101 or Crimestoppers anonymously on 0800 555 111.