Robert Vadra, husband of Priyanka, and Board of control for cricket in India (BCCI) official and Rajya Sabha member Rajiv Shukla also left alongwith Rahul and Priyanka.
All the four left for Mumbai enroute to Karachi.
Meanwhile, Law Minister Arun Jaitley will also leave for Karachi on Friday to watch the first One-day International cricket match between India and Pakistan on Saturday.
Jaitley, who has been invited by the Pakistan Cricket Board (PCB) along with 200-odd guests recommended to it by the BCCI, would meet the Indian team later in the day.
When asked if his visit is official or private, Jaitley, who is also chairman of Delhi District Cricket Association (DDCA), said, "it (visit) is completely private".
India tours Pakistan after a gap of nearly 15 years to play five One-day games and three Tests on their 40-day tour which will begin with the first ODI in Karachi on Saturday.