The permission comes with a series of conditions, including the use of a diplomatic passport and the submission of detailed information about his proposed trip.
SC sets conditions
A bench headed by Chief Justice of India Surya Kant permitted Banerjee to travel overseas for his medical treatment.
The court, however, directed him to provide details of his travel itinerary, overseas accommodation, the doctor and hospital where he will receive treatment, and his flight arrangements.
Banerjee has been permitted to travel only on his diplomatic passport.
The court also said investigating agencies could use the information supplied by Banerjee as part of their investigation.
At the same time, it directed that the details must be kept confidential.
The Supreme Court's order came after Banerjee challenged a Calcutta High Court decision that had prevented him from travelling abroad in connection with a case involving allegations of hate speech.
Plea earlier rejected at Calcutta HC
The latest Supreme Court order follows a hearing before the Calcutta High Court last week, where Banerjee's request to travel abroad for eye treatment was rejected.
The High Court had directed Banerjee to appear before a medical board at the state-run SSKM Hospital in Kolkata.
The board was expected to assess his medical condition and determine whether treatment abroad was necessary or whether his condition could be treated in India.
During the proceedings, Justice Saugata Bhattacharya asked Banerjee's counsel whether the TMC leader would agree to an examination by a medical board headed by the head of the Ophthalmology Department at SSKM Hospital.
After consulting Banerjee, his lawyer said he wanted to be examined by a doctor of his choice instead.
Banerjee subsequently informed the court that he was unwilling to appear before the medical board.
The High Court then dismissed his plea seeking permission for overseas treatment, holding that the medical assessment was necessary to determine whether treatment outside India was required.
'Right to choose medical treatment'
While granting permission, the Supreme Court stressed an individual's right to travel abroad and choose medical treatment.
The court observed that "every individual has a right to travel abroad" and "every individual has a right to choose his medical treatment".
The Supreme Court nevertheless imposed safeguards because Banerjee's foreign travel is linked to an ongoing legal matter.
The requirement to submit his itinerary, medical details, accommodation and flight information will allow the investigating agencies to track the proposed travel arrangements while maintaining confidentiality over the information.
3 weeks of overseas treatment in September
Banerjee will be allowed to remain abroad for three weeks in September.
The Supreme Court's permission is specifically linked to his eye treatment and does not remove the other legal proceedings involving him.
The TMC leader had approached the Supreme Court after the Calcutta High Court refused to relax the restriction on his foreign travel.