In a statement on Saturday, poweroutages.us., a website which records and aggregates live power outage data from utilities all across the US, said that over 586,600 outages were reported in Louisiana, 103,598 in Texas and 67,873 in Mississippi, reports CBS News.
Baton Rouge, the state capital of Louisiana, had the most outages with 64,000 Entergy customers and 36,000 DEMCO customers in the dark.
Entergy and DEMCO are the two largest energy providers in the state.
The Category 2 hurricane lost intensity as it made landfall on Friday night, but not quickly enough to make a significant difference in its immediate effects.
It caused fresh destruction in communities still reeling from the Category 4 hurricane Laura, which made landfall in Louisiana in August, killing over 40 people.
Meanwhile in its latest update, the National Hurricane Center (NHC) said a few tornadoes were possible in Alabama, eastern Mississippi, the Florida Panhandle and western/central Georgia.
Delta is also expected to dump another 2 to 5 inches of rain in Louisiana, Arkansas and Mississippi.
"These rainfall amounts will lead to flash, urban, small stream, and minor river flooding," CBS News quoted the NHC as saying.
Delta is the 10th named storm to make landfall in the US in a single hurricane season, an all-time record.
It continued the record-breaking theme of the current hurricane season, becoming the earliest storm to be named Delta.
The Greek alphabet is tapped for names after the pre-determined 21 names have been used.
The previous record-holding Delta storm formed on November 15, 2005.