The centre of the storm was last reported as being about 100 km from the Haitian capital, Port-au-Prince.
Aid groups warn that some 400,000 Haitians still living in makeshift camps after the deadly earthquake of 2010 are extremely vulnerable.
Forecasters say Isaac could cause life-threatening flash floods and mudslides in Haiti and the Dominican Republic.
The United States National Hurricane Centre (NHCi) predicts that the storm will move near or over Cuba later on Saturday and approach the Florida Keys on Sunday.
The storm could pose a potential threat to Florida during the US Republican National Convention.
Tropical Storm Isaac is no longer expected to become a hurricane as it hits the island of Hispaniola – the island shared by Haiti and the Dominican Republic – but the near-hurricane strength winds and rain have the potential to cause great destruction, especially in Haiti.
“These rains could cause life-threatening flash floods and mudslides,” the NHC warned.
In Haiti, people living in the makeshift squatter camps were “amongst the more vulnerable, should the storm hit the city”, humanitarian group World Vision said.
“Without a stable sanitation system or permanent housing, heavy rain and wind can create much larger problems like disease from water contamination,” the group’s Haiti director Jean-Claude Mukadi was quoted as saying by the AFP news agency.
The country’s president, Michael Martelly, has toured some of the camp sites.
“It looks like the south coast is going to get hit, but again we’re so fragile here in Port-au-Prince that just some rain can cause a lot of damage,” Associated Press quoted him as saying afterwards.
Isaac is also expected to bring rain and wind to nearby Puerto Rico.
Several Cuban provinces are now on a state of alert, as are parts of the Bahamas and the Turks and Caicos islands.
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