Emily is threatening heavy rain and flooding on the island of Hispaniola, where Haiti and the Dominican Republic are situated.
That could be especially disastrous in Haiti, where hundreds of thousands of people are still living in camps because of last year’s earthquake.
The eye of the storm is likely to make landfall just north of Cabo Beata, on the southern tip of the Dominican Republic, on Wednesday.
Martinique and other Caribbean islands, including Puerto Rico and the US Virgin Islands, are also preparing to face heavy rain and flooding.
Tropical storm force winds extend up to 110 kilometres from the centre of the storm but the Miami-based National Hurricane Center said that one of its 'hurricane hunter' planes "finds Emily still poorly organised".
The storm passed by the French territory of Guadeloupe without causing great damage, officials say.