Mr Nirupam, a Congress MP, had questioned Ms Irani's credentials, allegedly saying: "You used to charge money to perform dance shows on TV. Now you are an election analyst."
Ms Irani sent a legal notice to Mr Nirupam.
"The BJP will protest against Sonia Gandhi if she doesn't investigate Sanjay Nirupam's comments against Smriti Irani. Sonia Gandhi should apologise. The BJP has taken this matter very seriously. Smriti Irani has sent a legal notice to Sanjay Nirupam for defamation," BJP spokesperson Ravi Shankar Prasad said today.
In Mumbai, the BJP's youth and women's wings staged a protest against Mr Nirupam. Around 300 activists took out a procession till the Congress leader's office.
The remark has also invited angry reactions online, with some pointing to Mr Nirupam's foray into television through reality show Bigg Boss.
(With inputs from PTI)