The actress was recently "scared" by an incident on the set of her new film Chalo Dilli, when a fake version of the insect was thrown towards her.
A source for the film's production team said: "A crew member threw a plastic cockroach on [Dutta]. And Lara, who otherwise is strong and controlled, got so scared that she practically jumped and ran helter-skelter, screaming [at the] top of her lungs.
"It was a side of Lara we had never seen before. Even the sight of a cockroach sends shivers down her spine."
Dutta, who once commented that she could never look cheap on camera, appears opposite Bheja Fry actor Vinay Pathak in the road movie.
The Housefull star was recently threatened with a boycott by the Indian media, after refusing to pose for photographs following her wedding.
Chalo Dilli is scheduled to be released on April 29.