Floyd died after a police officer knelt on his neck during an arrest in Minneapolis last week.
His death “is just a reminder of how little we’ve grown as a country from our original sin of slavery”, Clooney wrote in his column for the Daily Beast.
The actor also described the recent Black Lives Matter protests, which have taken place the world in response to Floyd’s death, as “the anger and the frustration we see playing out once again in our streets.”
“There is little doubt that George Floyd was murdered,” the 59-year-old said, before calling for “systemic change in our law enforcement and in our criminal justice system”.
“We need policymakers and politicians that reflect basic fairness to all of their citizens equally,” Clooney explained.
Nodding to the recent tweets of President Donald Trump, he continued: “Not leaders that stoke hatred and violence as if the idea of shooting looters could ever be anything less than a racial dog whistle. Bull Connor was more subtle.
“This is our pandemic. It infects all of us, and in 400 years we’ve yet to find a vaccine. It seems we’ve stopped even looking for one and we just try to treat the wound on an individual basis.”
The Ocean’s Eleven star concluded there was only one way to bring real change to the country.
“To bring lasting change: Vote,” he said.
Clooney has previously been vocal about Trump’s presidency, particularly after he was accused of being part of the “Hollywood elite”.