The storm left no major flooding, but the National Weather Service (NWS) New Orleans said Olga brought wind gusts of 40 up to 70 mph from coastal southeast Louisiana into southern Mississippi.
"These winds were higher than we expected, and we will be studying this storm to learn how we can better forecast situations in the future," the NWS said.
A wind advisory that could potentially knock out power remained in eastern Mississippi, according to NWS Jackson Meteorologist John Moore.
“Olga has dissipated but remnants are pushing north into Tennessee,” Moore said. “It should be out of state [Mississippi] by later Saturday.”
Tupelo Mayor Jason Shelton was trapped in his Mississippi home by a downed tree for 1.5 hours on Saturday and reportedly suffered injuries. He was taken out on a stretcher.
City spokeswoman Lucia Randle said the mayor was taken to North Mississippi Medical Center and was "under observation," but didn't specify his injuries.
Residents had also been alerted to multiple tornado warnings, and at least one twister touched down in Mobile, Ala.
Downed trees were a major issue.
In New Orleans, city officials said there were more than "25 reported tree emergencies." About 30 trees were removed from the Abita Springs, Bush, Covington, Hickory, Mandeville, and Talisheek areas.
The Louis Armstrong New Orleans International Airport suffered two power outages but said it was "fully restored" as of Saturday afternoon.
In Louisiana, nearly 70,000 buildings were without power at the peak of the storm.
Birmingham NWS Meteorologist Gary Goggins said winds that might blow up to 40 mph are a remaining hazard around Tuscaloosa, Ala.
The Associated Press contributed to this report.