The duo was in the city last week to attend an event and later flag off a women's rally, a press release said.
"We met the royal family of Jaipur while we were in the city. They were extremely gracious and friendly, " Kumar Taurani, managing director of Tips Industries, said in the release.
Maharani Padmini Devi of Jaipur played host to the actor and producer, who were overwhelmed after meeting her daughter, Princess Diya, and grandchild, 12-year-old Prince Padmanabh Singh.
"The young Prince Padmanabh was an absolute charmer. Jaipur is a beautiful city and I would love to go back and shoot there soon, " Vivek said.
"Prince", releasing April 9, narrates the story of a thief who wakes up one morning to realise that he has lost his memory and his life is at stake. It has been directed by Kookie V. Gulati.
Apart from Vivek Oberoi, the film also features Nandana Sen, Aruna Shields and Neeru Singh.