The cyclonic storm was centred about 1,105 km to 990 km from the ports of Bangladesh at 12 pm Friday, the Met Office said in a special bulletin.
All fishing boats and trawlers over the north Bay and deep sea have been advised to come close to the coast and proceed with caution. They are also advised not to venture into the deep sea.
Cyclones in the Arabian Sea and the Bay of Bengal are named by the World Meteorological Organization's regional cyclone agency ESCAP. The names of new cyclones are gradually fixed from a list of names given by the 13 countries in the region. The name 'Jawad' was selected by Saudi Arabia.
It is also likely to bring heavy to very heavy rainfall in the coastal areas and Gangetic parts of West Bengal, it said.
Its impact on Bangladesh will depend on the direction from which the cyclone crosses the coastline, according to meteorologists.
"The Khulna-Barishal region is likely to experience light rainfall on Friday and Saturday due to the cyclone," said Assistant Meteorologist Afruza Sultana.