Banerjee was apparently referring to the slogan of "Desh ke gaddaron ko" raised by Thakur during a campaign meeting for the Delhi assembly polls.
"How can a Union Minister continue in office after speaking such unconstitutional language? ... In Shaheen Bagh, there are lot of women who are sitting in protest and even in our state, they are holding sit-in protests at a few places. A central minister said that go and shoot them.
"After saying this how can he hold on to his position? In a democracy, you cannot just go and shoot people," the Trinamool Congress supremo said while addressing a party workers' convention in Nadia district's Krishnanagar.
Banerjee also lambasted Uttar Pradesh Chief Minister Yogi Adityanath for saying "people who will not listen to 'boli' (words of advice) will have to face police's goli (bullets)".
Describing BJP as a "feku party" which spins out "fake news", she accused it of "trying to divide people on the basis of religion" and "threatening them with guns and bullets".
"I was born in Hindustan, not in a nation governed by BJP, which attacks people with guns and bullets."
Delivering an election speech on January 27, Thakur had raised the slogan "Desh ke gaddaron ko" with the assembled audience responding in chorus "goli maaro saalon ko".
This prompted the Election Commission to slap a show cause notice on him before barring him from campaigning for the Delhi polls for 48 hours.
Predicting that the BJP will lose Delhi elections, Banerjee said the party was "shameless" and despite suffering a string of poll losses was still bringing anti-people laws.
( With inputs from IANS )