His coffin was taken from a church where it was on public display to be buried beside his mother.
A service was held at the Fountain of Praise church, attended by some 500 guests including politicians and celebrities, CBS News reports.
Minnesota Governor Tim Walz called on people to honour the funeral by observing silence for eight minutes and 46 seconds, the time Floyd was pinned to the ground before he died.
Floyd died in Minneapolis last month as a white police officer held a knee on his neck for nearly nine minutes, his final moments filmed on phones.
Democratic presidential candidate Joe Biden visited the dead man’s family to offer his sympathies on Monday.
Floyd’s death was “one of the great inflection points in American history”, Mr Biden later told CBS news.
Biden has sharply criticised President Donald Trump, who is standing for re-election as the Republican candidate on 3 November, accusing him at the weekend of making “despicable” speculative remarks about Floyd.
The Democratic politician was himself recently accused of taking black American votes for granted when he said African Americans “ain’t black” if they even considered voting for Trump. (Courtesy BBC)