The storm, which formed on Saturday morning, brought torrential rains to parts of Louisiana, Mississippi, Alabama and the Florida panhandle.
An advisory for the Carolinas on Monday from the National Hurricane Center warned of wind speeds of 40 mph (65 kph) on Monday, before Claudette was forecast to head toward the Atlantic Ocean.
On Saturday, wet conditions on Interstate 65 allegedly caused a van carrying children from a youth home to burst into flames and hydroplane, colliding with vehicles.
It was carrying children ages 4 to 17 from the Tallapoosa County Girls Ranch, a youth home operated by the Alabama Sheriffs Association.
Michael Smith, the youth ranch's CEO, said the van was heading back to the ranch near Camp Hill, northeast of Montgomery, after a week at the beach in Gulf Shores.
Candice Gulley, the ranch director, was the van's only survivor — pulled from the flames by a bystander. She remains hospitalised, and is in a serious but stable condition.
"Words cannot explain what I saw," Mr Smith said of the accident site, which he visited after travelling from Gulf Shores in a separate vehicle.
A coroner in Butler County, Alabama, confirmed that eight children were killed in the crash, 35 miles (55 kilometers) south of Montgomery.
Cody Fox, aged 29, and his 9-month-old daughter, Ariana, were also killed in the collision on Interstate 65. They were from Tennessee.
Additionally, a 24-year-old man and a 3-year-old boy were killed on Saturday in Tuscaloosa, Alabama, after a tree fell on top of the family home.
And in another incident, 23-year-old Makayla Ross died after her car ran off the road into a creek in DaKalb County.
Additional reporting by Associated Press.