With a video of the incident circulating on the Internet, the company in a statement said it has taken up the incident seriously.
"We are in the know of the incident and we have taken this up very seriously," FCA India said.
It further said: "The sequence of events is currently being investigated. Appropriate action will be taken once all facts are studied and considered".
In a separate statement, the company's dealer Landmark Group said: "It is unfortunate that a video is being circulated on social media relating to an incident that took place in our Delhi branch of Jeep showroom".
The Jeep vehicle line-up in India consists of the Jeep Wrangler, Grand Cherokee and the Jeep Compass.
Last week, FCA India had announced a recall of around 1,200 units of Jeep Compass for replacement of front passenger air bag.