Tropical Depression Nine strengthened into Tropical Storm Humberto on Friday night.
It is currently moving northwest towards Great Abaco island, one of the islands worst hit by Dorian.
About 1,300 people are missing in the Bahamas following the hurricane, while at least 15,000 are in need of shelter, food and medical care.
Humberto is due to cause strong winds and heavy rains on the islands, with some areas potentially seeing 15 cm (six inches) of rain and wind speeds of 45 km/h (30 mph).
The BBC Weather service has advised that Humberto could strengthen into another hurricane over the coming days, although this is not likely to happen until it has passed over the Bahamas.
Officials have warned that flooding from the fresh storm could hamper their rescue and relief efforts.