The complaint was filed by the president of a local organisation in Andheri police station, police said.
A TV channel had called Puri to join a debate about the Indian Motion Pictures Producers Association's (IMPPA) indefinite ban on Pakistani artistes from working in Indian projects after the Uri attack.
The complaint alleged that during the discussion, Puri said, "Who had asked soldiers to join the army? Who told them to pick the weapons?," police said.
The complainant also alleged that the actor had insulted the Indian Army and the nation and demanded to register an FIR against him for sedition under section 124 (A) of the IPC, police said.
"We have received an application (complaint) from a person against Om Puri. Mumbai police is inquiring the matter. Further action will be taken based on the probe", said Deputy Commissioner of Police Ashok Dudhe.