INS Sumitra is involved in a major Search and Rescue (SAR) operation 90 miles south of Bangladesh's Chittagong.
18 people have been rescued till now and the operation is still in progress.
The people trapped, had been blown away from shore and coastal dwelling units due to Cyclone Mora.
One man's pulse and heart beat could not be traced after being rescued. However, he was revived and is currently on ventilator.
Massive evacuation is underway in Bangladesh as severe cyclonic storm 'Mora' hit Chittagong on 30 may.
The severe cyclonic storm MORA over northeast and adjoining east central Bay of Bengal moved further north northeastward with a speed of 28 kmph, and lay centred at 0230 hrs IST on 30 may.
Heavy rainfall is being reported in Chittagong. Deputy Commissioner Zillur Rahman Chowdhury has said about 30,000 people have taken up refuge at the hundreds of storm shelters near the coast
The Met office has advised to hoist great Danger Signal No 10 at coastal areas including Chittagong, Cox's Bazar, Khulna, Satkhira and the two coastal ports in Mongla and Payra.
Mora was centred at around 385km south of Chittagong port and 305km south of Cox's Bazar port around 7pm on 29 may, said Bangladesh Meteorological Department.
The Indian Navy on 29 may had said that it has kept its Eastern Fleet ships at the highest level of readiness to render assistance to Bangladesh if required.