NHS Greater Glasgow and Clyde (NHSGGC) said the incidents included staff being followed, secretly photographed and harassed.
The policy was put together by Strathclyde Police domestic abuse task force and Action Scotland Against Stalking.
It outlines how to deal with stalking, how to support and protect staff and ways of recognising dangerous or threatening behaviour, ranging from sexual harassment and property damage to "whispering campaigns" against staff.
The policy also sets out measures that can help protect staff from stalkers, including mentoring and "buddying up" with colleagues at work.
The Health Board will also offer staff who work on their own GPS "panic buttons" that transmit the precise location of a person in an emergency.
Kenneth Fleming, NHSGGC head of health and safety, said: "This new policy will raise awareness of the issue among staff, managers and human resources personnel and provides guidance and a framework for recognising stalking, supporting staff affected and provides managers with the know-how to safely manage any incidents which are affecting their staff."
Ann Moulds, of Action Scotland Against Stalking, said stalking was a "serious form of violence".
She said: "Workplace stalking frequencies have without doubt been underestimated. The structure of the working environment can make it easier for a stalker to track and pursue their victim with relative ease.
"This is an excellent policy which will allow for early identification of stalking cases, staged interventions through ongoing case management thereby offering the victim protection and support."