The incident occurred at around 12:15 local time, an hour after a curfew that was imposed on the city after five nights of protests.
Reports say that local police officers and the National Guard were attempting to break up a gathering in a parking lot outside a grocery store when they were fired upon from the crowd. They returned fire, and one person was at some point shot dead.
The chief of the Louisville Metropolitan Police Department, Steve Conrad, told local media that several persons of interest are being interviewed. Futher information is expected later today.
Sunday night's shooting comes just days after seven people were injured by gunfire at another protest in the city, this one focused on the killing of Breonna Taylor, a black woman shot in her apartment by police in March during a drug raid.
The details of the raid are still a matter of dispute, and the officers involved claim that Ms Taylor was shot inavertently.
The shots fired at that protest came from within the crowd, and no police officers were reported to have fired their guns.
The killing of Mr Floyd, who died after a police officer knelt on his neck for several minutes, has sparked protests across the US, many of which have seen vandalism and looting, with police using pepper spray, flash grenades and rubber bullets.
Several cities have called in the National Guard and imposed curfews to try and control the situation.
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