The case was filed in the court of the chief judicial magistrate and has been listed for hearing July 25.
The petitioner, lawyer K.C. Tripathi, sought the arrest of Vaidik, who is also a journalist, for sedition.
Tripathi argued that the journalist had committed a crime by meeting a terrorist accused of masterminding the 2008 Mumbai terror attack that left 166 people dead.
Vaidik met Saeed in Lahore where he had gone as a member of an Indian delegation that also included Congress leaders Mani Shankar Aiyar and former external affairs minister Salman Khurshid.
Vaidik's meeting triggered outrage, with the government denouncing the meeting.