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The storm is still packing maximum sustained winds of 60 mph and is located over northeast Georgia, heading northeast at 39 mph.
The National Hurricane Center (NHC) has warned that damaging winds, especially in gusts, are spreading "well inland" across portions of Alabama and northern Georgia. Those winds will shift into eastern Tennessee, the Carolinas and southeastern Virginia.
"Wind gusts could be especially severe across the southern Appalachian Mountains," the NHC said.
Zeta's gusts have already caused widespread power problems across the South.
By dawn Thursday, over 2 million customers across Louisiana, Mississippi, Alabama and Georgia were without power, according to the website PowerOutage.US.
Georgia saw the greatest number of outages, with over 1 million customers impacted in the northern part of the state as numbers continued to grow.
Louisiana, where Zeta made landfall, had over 500,000 customers without power in the southeastern portion of the state that includes the New Orleans metropolitan area. Alabama and Mississippi had outages that reached well over 200,000 customers, according to PowerOutage.US.
In Louisiana and Mississippi, utility Entergy said it has mobilized a storm team of more than 4,000 workers to handle storm response.
Much of New Orleans and the surrounding area were without power Wednesday night. The storm's winds whipped through the city, causing a structural collapse that injured one person.
New Orleans Mayor LaToya Cantrell implored residents to stay home and let city officials assess the damage.
“Although we have made it through, we have been damaged, we have been hit,” she said.
A 55-year-old man in Louisiana died after a coroner said he was electrocuted by a downed power line in New Orleans, and officials said life-threatening conditions would last into Thursday.
Entergy warned the most dangerous part of the storm is "just after it has passed."
"Stay away from downed power lines and areas of debris," the utility said.
Those who lost power in Zeta may have to wait days for the lights to be back on.
"Based on historical restoration times, customers in the direct path of a Category 1 hurricane can experience outages up to seven days and outages up to 10 days for a Category 2 hurricane," the utility said. "While 90% of customers will be restored sooner, customers should plan for the possibility of being in the hardest-hit area."
Louisiana Gov. John Bel Edwards was expected Thursday to tour the coastal regions hardest hit by the storm. During a radio interview Wednesday evening, Edwards said the wind had caused extensive structural damage.
In Georgia, utility Georgia Power advised that due to already saturated soil, the high winds of Zeta are likely to bring down trees.
Severe thunderstorms will be possible, including brief tornadoes to the east of the center of Zeta as the storm moves north. Heavy rain will also spread across a wide swath of the East with some areas receiving 1-3 inches. Flash flooding will be possible.
Fox News' Janice Dean and the Associated Press contributed to this report.