Hurricane warnings are in effect along parts of the Louisiana and Mississippi coast lines and a tropical storm warning is in place for Florida's western panhandle.
“As this moves its way into southeastern Louisiana, there very well will be locations such as New Orleans that could have winds gusting 60 to 80 miles per hour,” said Brittany Boyer, a meteorologist with AccuWeather.
Zeta could drop up to six inches of rain in the New Orleans area.
But because of its speed, the region could avoid the risk of flooding.
Zeta made landfall as a hurricane earlier this week on Mexico's Yucatan Peninsula.
Residents there are recovering from storm surge and strong winds that brought down trees.