Red paint was splashed on Colston's face and a protestor put his knee to the statue's neck to recall how Floyd - an unarmed African American - was asphyxiated by a white policeman in the United States city of Minneapolis last month.
During the protest, some attendees tied a rope around the memorial of Edward Colston in Bristol, where the bronze statue has stood since 1895.
According to police reports, around 10,000 people attended Bristol's Black Lives Matter demonstration on Sunday.
It is believed to have sold around 100,000 west Africans in the Caribbean and the Americas between 1672 and 1689.
Protesters in Bristol have pulled down a controversial statue of a 17th century slave trader.
In 2016 Oriel College chose to keep the statue despite widespread student demands to remove it. Campaigners from the Rhodes Must Fall group argued the row illustrated Britain's "imperial blind spot".
The toppling of Colston's statue has prompted a heated debate among the broader public over the role of monuments in memorialising and celebrating the role of historical figures, especially those with tarnished records on race.
Speaking after the demonstration, superintendent Andy Bennett vowed there would be an investigation into the 'act of criminal damage, ' near Bristol Harbourside, where slave ships once docked centuries ago.
However, Colston made an unknown percentage of his wealth out of the slave trade .
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And on Monday he said the Colston statue should not be recovered after demonstrators threw it into a river.
Some said that when they put "Statue of Edward Colston" on Google Maps, it showed the area as "permanently closed".
Colston was also a Tory member of parliament and philanthropist, donating huge funds to support schools, hospitals, almshouses and churches in Bristol.
"We're preserving #BlackLivesMatter signs left at the former site of the #Colston statue so we can tell the story of this historic moment for our city", Mr Rees tweeted.
She flagged that authorities agreed to add Colston's involvement in the slave trade on the statue's plaque in 2018 but that no changes had yet been made.
A small group of protesters pulled down the statue of General Williams Carter Wickham, erected in 1891.
However, at the time that I looked, the updated location of the statue had reverted back to its original spot. where the statue is no longer located.
Williams underlines that the Colston statue's case epitomises "so numerous big questions we must confront in this country as so much of this country's riches gained in the past stem from the misery of others".
In Brussels, Belgium, 30 000 or so signatures have been collected by two petitions calling for the removal of all statues and monuments dedicated to King Leopold II. In 2017, it was announced that Colston Hall - a music venue in the city - would be renamed ahead of the events space reopening in 2020.