In a letter to Shah, Congress general secretary KC Venugopal said Gandhi's security was compromised on a number of occasions after his rally entered Delhi.
Gandhi, a former Congress president, is entitled to Z+ or the highest level of security.
Venugopal wrote to the minister that the Delhi Police, which falls under the central government's jurisdiction, was a "mute spectator" when Gandhi's security was compromised.
The Bharat Jodo Yatra, which is spearheaded by Gandhi, began from Kanyakumari in September.