Ten policemen of the 28-year-old MP's convoy were also injured.
"Abhishek Banerjee was injured when the vehicle he was travelling in met with an accident on the Durgapur Expressway near Singur in Hooghly district. He was immediately taken to a hospital," ADG (Law and Order) Anuj Sharma told PTI.
He is stable now, Banerjee said.
Two special teams from CID and Kolkata Police are inquiring into the cause of the accident, a senior CID officer said.
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"President Pranab Mukherjee called me up and inquired about Abhishek's health condition," she said adding, "Abhishek is stable now. Doctors are investigating the nature of his injuries."
Referring to earlier incidents in which other cars had came close to Abhishek's convoy, she said police would investigate why such things are repeatedly happening.
Abhishek, also the TMC youth wing president, was returning from Murshidabad district after a party programme.
He was rushed to Kolkata and admitted to Belle Vue Clinic.
Hospital sources said a medical board has been formed for his treatment, while some medical tests and investigations have already been conducted.
"Mr Banerjee's injuries are being investigated thoroughly. He has been taken to the ITU and a CT Scan and other tests have already been done. After the reports are available, a medical bulletin will be released," Belle Vue Clinic CEO P Tondon said.
While the Chief Minister was keeping in touch with the hospital authorities, party leaders rushed to the hospital to enquire about Abhishek's condition and treatment.
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West Bengal Governor Keshari Nath Tripathi visited the nursing home later in the evening and spoke to Chief Minister Mamata Banerjee to enquire about Abhishek Banerjee's health conditions.
He spoke to the Chief Minister and expressed his concern about the TMC MP's health and wished a speedy recovery, a message released from the Raj Bhawan tonight said.