Images may have been circulated via social media.
Part of the nursery at Gael Scoil on the Green Road was damaged by fire on Sunday night.
Staff reported damage to tyres and cones at the school.
Speaking on Kildare Today, Garda Shane Smyth appealed for witnesses to come forward.
He said images may have been circulated via social media.

Kfm Weekend Obituary Notices
Two Men Charged In Connection With €4 Million Cocaine Seizure In Kildare And Wexford
Driving Testers At RSA Balloted For Industrial Action Over Concerns About Uninsured Vehicles
Homes Undelivered After Substantial Deposits Paid, Kildare Council Warns Of Potential Unauthorised Works
Over 1,000 E-Scooter Fines Issued As Kildare TD Calls For Tougher Penalties After Child Injured
Celbridge "Affordable" Homes Come With Council Equity Stakes
M4 Access Road To Castletown Will Reopen Next Week
Lucan Woman Pleads Guilty To Sending Threatening Messages To Tanaiste