The incident occurred on Gobinda Khatik Road in the Tangra area around Tuesday-Wednesday midnight when the victims were returning with other members of the family from a marriage ceremony.
Police on Wednesday arrested two persons and seized the ambulance.
The woman said the ambulance came beside them at a high speed and screeched to a halt. She could hear one of those inside the vehicle telling the other person: "Drag her in."
"There was one person in the ambulance apart from the driver. I got panicked on hearing what they were saying. Then one of them tried to drag me inside by pulling my left arm. When I shouted, my father-in-law and others rushed to save me. My father-in-law stood before the vehicle.
"When those inside the vehicle found the situation getting messy for them, they drove at a high speed, running over and dragging my father-in-law," she said, still trembling in fear.
The man was rushed to the state-run Nil Ratan Sarkar Medical College Hospital where doctors pronounced him dead.
The woman said she had not seen the assailants earlier. "But if I see them again, I'll be able to identify them," she said.
A local person who saw the incident said the vehicle had dragged the woman's father-in-law with such ferocity that all his clothes were torn apart.
"When we rescued him, he had virtually nothing on," he said.
City police's Joint Commissioner, Crime, Murlidhar Sharma said Abdur Rahaman, 26, and Tajuddin, 20, were arrested after studying CCTV footage of the ambulance in the area.
"Rahaman, a resident of Daulatpur village in 24 Parganas (South) district, was in the driver's seat. Tajuddin hails from Nauhazari in the same district."
There have been a number of incidents of women including actresses and models getting harassed in Kolkata over the past few months. One of the victims was former Miss India Universe Ushoshi Sengupta.
A group of bike-borne youths had beaten up the driver of Sengupta's cab after one of their two-wheelers hit the car. The youths then followed her, threw stones at the cab and tried to snatch her phone to delete the video she had taken of the incident.
Popular Bengali television actor Swastika Dutta had a harrowing experience, when an app cab driver "pulled" her out of the vehicle, threatened and "abused" her when she was going for a serial shoot.
A week prior to Dutta's bitter experience, TV actress Juhi Sengupta alleged that she along with her parents was harassed and heckled by employees of a petrol pump. Her father, a senior citizen, was even pushed by the employee during the altercation.
In December last year, a group of youths in a car chased an actress and made indecent gestures at her using cuss words.
( With inputs from IANS )