At least 25 people were injured in the incident, six of whom are critical. They are currently being treated at Jalpaiguri Sadar Hospital.
"As soon as the main gate of Dhupguri Health Centre was opened, several people tried to get inside the facility pushing each other. A stampede-like situation arose there. Several women were injured. We are probing the matter," a senior officer said as reported by PTI.
Locals said hundreds of people had been queuing outside the centre since morning and social distancing protocols were heavily flouted.
Asked about what led to the stampede-like situation, the officer said, "We are probing the matter. According to a preliminary investigation, those who were in the queue tried to enter the centre in the apprehension of a shortage of vaccine doses."
Soon after the incident, the inoculation programme at the centre has been stopped.