Chopra arranged the vehicle to give the 'Part of Me' star a taste of travelling in the three-wheeled transport, according to The Hollywood Reporter.
"I really liked Perry's performance and her costume, which was like a take on Princess Jasmine from Aladdin," Chopra said.
"It was fun to hang out with Katy the next day. We did lunch, and then I took her out for a rickshaw ride as I wanted Katy to have a typical Indian experience."
Perry was in the southern city of Chennai to perform at the opening ceremony of the Indian Premier League cricket tournament.
The US singer had previously only visited the north of the country with former partner Russell Brand, when they got married in a private ceremony in Rajasthan in 2010.
Perry wore a floral outfit, and Chopra a sleeveless green Vanessa Bruno dress for the shopping trip.
The Bollywood actress has announced plans to release her debut single within the next few months.
Watch the video for Katy Perry's Bollywood remix 'Bolly Gurls' below: