The actor plays a geek who lies compulsively in Abbas Tyrewala's Jhootha Hi Sahi.
According to Bollywood Spice, the female fan called in during a promotional radio phone-in to shout at the star.
The show's producer Madhu Mantena told the site: "John answered this one call, and the girl really yelled at him. I could see that he was very shocked.
"John was visibly upset with the call. However, he tried to calm the girl out and counsel her to the best of his efforts."
The romantic comedy sees Abraham playing a man who accidentally receives the final call from a suicidal woman.