The doctor, a resident of Tiljala, on Friday received a call from the woman, who complained of excruciating chest pain and promised him high fees for a house visit.
When the doctor went to her Dum Dum residence, the woman handed him an old prescription. When the doctor was taking a look at it, the woman suddenly embraced him.
Three youth then rushed into the room and surrounded the doctor, claiming they were policemen, and accused him of behaving indecently with the woman.
One of the youth was in police uniform.
They undressed the doctor, clicked his photos with the woman, and demanded Rs 10 lakh in cash. They threatened to make the pictures viral unless he paid up.
The doctor pleaded that he was not carrying so much money, and handed them Rs 15,000.
He promised to pay the remaining amount from the cash at home and was driven by two of the youth to his residence.
However, the doctor managed to contact the Tiljala police station, and officers rushed in to pick up the two youth.
The woman and the other youth surrendered in the Alipore court on Saturday.
The source said a police uniform was seized from the house of one of the accused.
The four accused were allegedly involved in an extortion racket.
( With inputs from IANS )