Deputy Commissioner of Police Amitabh Gupta told reporters here the two men were connected with the television industry and one of them knew Irani professionally.
According to the police official, one of the arrested persons was a scriptwriter who had written television serials for several companies.
He said the threats were made to Irani for professional reasons. Gupta did not elaborate on this. He also did not reveal the names of the arrested persons.
Earlier this month, Irani had filed a complaint with the Mumbai police after receiving threatening calls from unknown persons.
The actress, who contested last year's parliament elections as a Bharatiya Janata Party candidate, had alleged that the callers abused her in communal terms.
Irani told journalists here that the threatening calls were being made to her for several weeks. After dismissing the calls as pranks from professional rivals, she opted to go to the police when the calls continued, Irani added.