Kapoor was forced to call security after the woman scaled his apartment block this week, according to Mumbai Mirror.
A source close to the star told the paper: "Shahid, who is aware of her background, has been sensitive enough to ignore these incidents so far, but Wednesday night was a little serious and he has decided to highlight this as a security breach with his society.
"In fact, a few years ago, she made her debut in a B-grade flick, where her role was drastically reduced. It was a huge blow for her."
He added that the woman, who is in her early 30s, had frequently "popped up near the gate and blocked [Kapoor's] path".
Kapoor has most recently been romantically linked with former model and Rockstar actress Nargis Fakhri.
He recently committed to his first action film Vettai.