As many as 42 people have been afflicted with the influenza while there have been two deaths in Kolkata so far.
"The total cases are 42 till Wednesday. No additional deaths were reported," B. R. Satpathi, director of health services, told IANS.
Tests were being conducted at the National Institute of Cholera and Enteric Diseases (NICED) facility in Beleghata.
"Additional positive cases might come in later today (Wednesday)," he said.
The official said oseltemavir tablets and masks are in stock.
Hospitals and medical colleges have been asked to remain extremely watchful.
During the period Jan 1 to Feb 10, in India the total number of H1N1 cases was 5,157 and the number of deaths was 407, the health ministry said.
Most cases were from Delhi, Gujarat, Rajasthan, Karnataka, Madhya Pradesh, Maharashtra, Tamil Nadu and Telangana, whereas the deaths were largely from Maharashtra, Madhya Pradesh, Gujarat, Rajasthan and Telangana.