The instruction went out this week to pupils at Balwearie High School as attempts were made to tackle the problems at the Tiel Bridge which they use as a shortcut to Invertiel Terrace.
Attempts to put barriers up to stop access have not been successful, and work is in hand to establish who owns it - and how it can be made safe.
The issue has been raised several times by Councillor Kathleen Leslie, whose Burntisland., Kinghorn and western Kirkcaldy takes in the area.
She met recently with the local Tenants and Resident Association and officers, and also contacted the school.
Balwearie has now written to pupils, stating: “Pupils taking a short cut to Invertiel Terrace must not use the bridge over the Tiel Burn.
“It is unsafe and could lead to someone being seriously injured.”
Cllr Leslie is hopeful work can begin in the autumn.
In an update on her Facebook page, she added: “This has been an ongoing issue.
“There are attempts to establish who the landowner may be, and also what can possibly be done to address the state of the bridge.
“Attempts by Fife Council to close off access to the bridge have previously been met with the barriers being pushed over into the water.
Cllr Leslie added: “This route is used by some pupils as a shortcut.
“Not only is there a gap on the bridge but the side fencing has also fallen away in parts. There are also nails sticking through the wood “