Police were called to HMP Kilmarnock, located on the town’s Mauchline Road, at around 7.30pm on Friday after a number of vehicles in the grounds were set alight.
No-one was injured in the incident, but enquiries are continuing in a bid to track down the culprits.
Efforts are continuing in a bid to trace the occupants of a dark-coloured car seen leaving the scene after the blaze broke out.
Detectives are scanning CCTV footage for further clues and appealing for people who may have witnessed the incident to come forward with any information that could help investigators.
Detective Inspector Ewan Bell said: “I’m sure someone will have seen or noticed this dark-coloured car as it sped off from the prison car park.
“All of the cars involved have been extensively damaged and I am appealing to people who were in the area around the time of the incident to contact us.
“Also, I would appeal to any motorists to check their dashcam footage as it may have captured an image which could assist us in our enquiries.”
Extra officers are being deployed to patrol the area to help provide reassurance to the local community.
Police are encouraging locals to approach the teams to discuss any concerns they may have.
Anyone with information is asked to call Police Scotland on 101, quoting incident number 3428 of 23 April.
Alternatively, details can be reported anonymously through the Crimestoppers hotline on 0800 555 111.