Of the the nine babies, who died between Wednesday evening and Thursday morning, seven were aged between one and 26 days while two others were between the ages of six and eight months, hospital sources said.
Six of them died in the newly-opened Sick New-born Care Unit in the hospital where only critical patients are admitted.
Three others died in the general paediatric ward. All of them were brought from rural hospitals with complications of low birth weight and varying degrees of breathing trouble.
West Bengal has been beset with children's deaths in hospitals across several districts since early last year.
Between Oct 25 and 28 last year, 16 babies died at the BC Roy Children's Hospital, the only children's referral hospital in Kolkata.
On July 18 last year, 18 infants had died there. The Burdwan Medical College and Hospital had reported 12 infant deaths on October 27-28, last year.