The fire was lit at around 10.30 on Thursday, June 24, in a storage area within a property on Orchard Street.
The Scottish Fire and Rescue Service attended and got the blaze under control, no injuries were reported.
Police are now appealing for anyone with information on this incident to come forward and said that if the SRFS had not put out the fire quickly, it could have been much worse.
Detective Constable Gary Bruce, of Paisley CID, said: “There are a number of derelict properties in this part of the town and vandalism and fire setting is becoming a problem.
“This kind of behaviour will not be tolerated. In this instance someone has entered the empty property and started a fire on the first floor inside a storage cupboard.
"Fortunately no one was injured but this could have been much more serious if it had not been put out quickly.
“We would like to speak to anyone who saw anything suspicious around the time of this incident, and we are also keen to speak to anyone who may have been driving in the area and has dash-cam footage that might assist with our enquiries.”
If you have any information on the incident you should call Police Scotland on 101, quoting incident number 3183 of Thursday, June 31.
If you have information but would like to remain anonymous you can call Crimestoppers on 08000 555 111.