She told the Milngavie Herald she was “terrified” after being followed by the man as she walked during daylight hours in a boardwalk area near South Lodge car park.
The woman, who does not want to be named, said she knows of others it has happened to in the same area.
The latest incident took place a couple of weeks ago.
Police have urged anyone who has seen anything suspicious to get in touch with them, adding they wanted to reassure women any reports will be “taken seriously and thoroughly investigated.”
Female employees of East Dunbartonshire Council work in the area and the council are assisting police with their inquiries.
The male has been described in his late 20s or early 30s.
The woman told the Herald: “There have been three women affected at least that I know of, and the last one was about a week or two ago.
"I was terrified. I just don’t want anything to happen to anyone. This guy could escalate things.
"I also thought ‘how many other women has this happened to’?
"You don’t want to scare people but you want them to be aware. I would want to know if it had happened to someone else.
"There is a wooden boardwalk that goes through this part of Mugdock Wood and it was in this big wooded area that he followed me.
"He came off the path and I saw that he was half hiding and he performed an indecent act. Other women said the same thing.
"He then appeared to wait for me at the top of a hill and I phoned someone and asked them to stay on the phone. I cut back across another way and found someone and asked them if I could walk with them as this man was following me.”
Depute Chief Executive, Ann Davie told the Herald: "We are aware of these reports and are currently assisting Police Scotland with their enquiries."
A Police Scotland spokesperson said: “We received a third party complaint about potentially suspicious behaviour in Mugdock Country Park in early January and efforts have been made to engage with the original complainer to establish more detail.
“We would urge anyone concerned about any potentially suspicious behaviour to report this to police at the time.
“Your reports will be taken seriously and thoroughly investigated.”