Jane Frith has ruled that the Royal High's back gate on to Queensferry Road will be locked after intruders were spotted on the school's CCTV cameras.
Some bikes which were locked up inside the school grounds have been damaged.
In a message to staff and pupils, Ms Frith said: "Could staff and pupils please note that in the last week or so intruders have been in the school grounds on at least two occasions and damage has been caused to bicycles left locked up outside. The police have been informed.
"Please make sure that bikes are secured at all times.
"If anyone notices intruders in the grounds, inform a senior member of staff or one of the janitors straight away."
A council spokesman said: "Steps have been taken to tighten security after some damage was caused to pupils' bikes."