At least 1,419 people are known to have died in the 7.2-magnitude quake. More than 6,900 were injured, and an unknown number are still missing.
Tropical Depression Grace is expected to dump up to 25cm (10 inches) of rainfall over the worst affected area.
It is feared the deluge could trigger landslides.
Social media footage showed heavy rain pouring over the island’s east, with the quake-hit west next in its path.
Roads already made impassable by the quake could be further damaged by the rains, so aid teams are racing to get essential provisions to the quake-hit region.
Search and rescue teams have been arriving from the United States and Chile, with more on the way from Mexico. Cuban medical teams are already in Haiti and helping people.
Humanitarian organisations say survivors need drinking water and shelter. More than 30,000 families have reportedly been left homeless.
Homes, churches and schools were among buildings flattened in the quake. Some hospitals were left overwhelmed and in need of supplies as they struggled to treat the injured.
The earthquake compounds problems facing the impoverished nation, which is already reeling from a political crisis following the assassination of its president last month.
The south-west of Haiti appears to have suffered the worst of the damage, especially around the city of Les Cayes.
Source: BBC News