Som, who is an accused in a riot case himself, said: "The women sitting on protests have no work, a probe is needed to find out the source of funding of these protests. As far as people like Sharjeel Imam, who talk of breaking India, are concerned, such people should be shot dead publicly."
Imam, a JNU student is in police custody following his controversial remark about "cutting off Assam" from India.
Som's statement came in the context of anti-CAA protests at Delhi's Shaheen Bagh and Lucknow's Clock Tower, where hundreds of women have been staging a sit-in against the new citizenship law for over a month.
On Thursday, women in Aligarh also joined in by sitting on an indefinite dharna at Eidgah, even as the police booked 250 of them for unlawful assembly.
The MLA's reaction came a day after a gun-wielding man opened fire on protesters near Jamia Millia Islamia, injuring a student.
Som, who is not new to controversies, had earlier called Owaisi an agent of Pakistan for opposing the Citizenship (Amendment) Bill in Parliament. He also attacked the Congress over the issue, saying that both the Congress and Owaisi 'should go to Pakistan'.
"Both Congress and Owaisi will have to go to Pakistan if they do not change their attitude especially when a Bill is being introduced for the welfare of our country...
"The Congress and Owaisi eat and breathe in our country but they speak on the political and diplomatic line that suits Pakistan," he had said.
Som is known for his extreme views and is an accused in the 2013 Muzaffarnagar riots.
( With inputs from IANS )