The incident occurred on Tuesday evening when Banerjee was on her way to inaugurate a Durga Puja idol at the Kalighat Milan Sangha club near her residence.
In a complaint, Rajya Sabha MP Dola Sen alleged that the woman in an intoxicated state, hurled abuses at Banerjee and attempted to approach her aggressively while carrying a knife.
The move comes days after West Bengal Chief Minister Adhikari claimed that she had faked her leg injury during the 2021 Assembly election campaign in Nandigram.
Addressing a press conference at the state secretariat Nabanna, Adhikari said the investigation would be initiated after the October 6 bypolls in Nandigram and Rejinagar Assembly constituencies.