Forecasters say they expect the storm to strengthen into a hurricane during the day Tuesday, and to continue building until it makes landfall late Tuesday or early Wednesday.
Areas along the northern Gulf Coast from Louisiana to Florida will begin experiencing tropical storm conditions early Tuesday.
President Barack Obama has declared a state of emergency in Louisiana, which was devastated by another massive storm - Hurricane Katrina - seven years ago.
Louisiana Governor Bobby Jindal urged residents in high-risk areas to flee.
The storm is already generating winds of 110 kilometers per hour, and forecasters say it could dump 30 centimeters of rain along the coast, with nearly 46 centimeters in isolated locations.
New Orleans Mayor Mitch Landrieu told residents to be prepared to live without regular water or power supplies for several days. He also urged them to leave if an evacuation order is issued.
Many people did not leave in 2005 when Hurricane Katrina struck the same area. Katrina ravaged New Orleans and much of the Gulf Coast, killing more than 1,800 people and leaving thousands more homeless. Wednesday marks Katrina's seventh anniversary.
Isaac battered eastern Cuba Saturday, after killing at least 19 people in Haiti, which is still recovering from a devastating 2010 earthquake. Two people were killed in the Dominican Republic. There were no reports of fatalities in Cuba.
