The complaint, lodged with the Deputy Commissioner of Police or DCP of New Delhi, demanded action against AAP convener and Delhi Chief Minister Arvind Kejriwal and lawmaker Amantullah Khan.
The Delhi BJP's good governance cell in-charge Shailender Singh lodged the complaint.
"The complaint has been received from Delhi BJP. We will enquire into it," said Madhur Verma, Deputy Commissioner of Police.
The AAP denied the charge, and said such "wild" accusations were a desperate bid of the BJP to mislead the public and divert attention from the crimes committed under its rule in Unnao and Kathua.
Describing the incident, he alleged that a group of four or five people wearing saffron gamchas and wielding swords had raised provocative slogans in front of a mosque immediately after a Ram Navami procession passed by it.
He alleged that the person leading the group was an AAP worker and was sent by the ruling party to incite communal tension in the national capital.