Around 300 BJP cadres participated in the procession which concluded at Nirupam's office in suburban Borivili.
Nirupam made an irresponsible statement at a time when crimes against women are rising and there is anger among people, a BJP functionary said.
He made the controversial remarks on Thursday during a debate on a news channel on the Gujarat assembly election results.
The Congress MP questioned the credentials of Irani to analyse poll results given her background as a TV actress.
He reportedly said "till some time ago you were dancing on the TV screens and now you have become a psephologist."