Tornadoes touched down in Louisiana, Texas and Mississippi.
On Sunday, the Mississippi Emergency Management Agenda confirmed deaths across three counties.
In Louisiana, a number of homes were destroyed in the city of Monroe, with the city's official social media account initially reporting only minor injuries.
The National Weather Service said severe thunderstorms were likely through late Sunday into Monday, in particular across parts of Mississippi, Alabama and Georgia.
"Strong tornadoes, widespread damaging winds, and large hail are all possible," the agency warned.
Sheltering amid the lockdown
In Mississippi, three deaths were confirmed in Jefferson Davis County, two in Lawrence and one in Walthall.
Last week, the American Meteorological Society issued guidelines for taking shelter during the coronavirus pandemic.
The vast majority of residents in the US are under stay-at-home orders.
"Do not let the virus prevent you from seeking refuge from a tornado," the association said.
It advised making shelter plans in advance in homes or with neighbours, friends or families.
Public shelters in many communities are closed because of lockdown measures. People were urged to still follow social distancing guidelines if they must seek safety in a public space like a school.
Alabama Governor Kay Ivey issued a state of emergency on Sunday that suspended Covid-19 mitigation measures that may have prevented people from gathering in public shelters in that state.