Floyd died in Minneapolis on May 25 after being arrested by a police officer who pinned the 46-year-old unarmed man to the ground for several minutes while kneeling on his neck.
Protests in the aftermath of Floyd's death lasted until the eighth day, while President Trump promised to deploy the military if the violence cannot be contained.
"Last week was so dark," Hamilton wrote on social media.
"I did not manage to keep my emotions. I felt so much anger, sadness and disbelief in what my eyes saw.
"I am completely overcome with rage at such a blatant disregard for the lives of our people. The injustice that our brothers and sisters face around the world time after time is disgusting and MUST stop."
READ: Premier League players urged to kneel to protest death of George Floyd
Hamilton has spoken out several times in the past week.
Six-time Formula 1 world champion called his sport's "biggest stars" who "remain silent amid injustice", and said in a separate post that he "was doing[es] not with those who loot and burn down buildings, but with those who protest peacefully. "
Since then, F1 has published an article saying[s] with all those who fight against racism in all its forms ", and several drivers also spoke.
READ: "I don't see racism in the NFL at all," says Denver Broncos head coach
"Unfortunately, America is not the only place where racism lives and we continue to fail as humans when we cannot stand up for what is right," said the Hamilton post on Tuesday.
"Please don't sit in silence, regardless of your skin color. Black Lives Matter."
Last week it was confirmed that the Formula 1 season will start with a double head in Austria on July 5. The races have been suspended since March amid the coronavirus pandemic.
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