Floyd, who is black, died in police custody in Minnesota after a white police officer kneeled on his neck for several minutes. The incident sparked protests in cities across the United States.
Minneapolis police officer Derek Chauvin was charged on Friday with murder in the death of unarmed 46-year-old Floyd.
Sancho, 20, went on to score a hat trick -- the first of his professional career -- in Dortmund's 6-1 victory. The England international was booked for removing his jersey -- an act that is against football rules.
Following the match, Sancho tweeted: "First professional hat trick. A bittersweet moment personally as there are more important things going on in the world today that we must address and help make a change.
"We have to come together as one & fight for justice. We are stronger together!"
Sancho's teammate Achraf Hakimi also lifted his jersey to reveal a similar message in support of justice for Floyd after scoring late in the second half of the rout.
Former NBA champion Stephen Jackson, Los Angeles Lakers forward LeBron James and teenage tennis player Coco Gauff have also spoken out about Floyd's death, with James tweeting "Why doesn't America love us!!!!???" on Sunday.
Taking to Instagram after the game, Thuram posted a photo of himself kneeling with the caption: Together is how we move forward. Together is how we make a change."
Protests have now spread to Europe, with people gathering in London and Berlin.
Gladbach tweeted an image of Thuram kneeling with the caption: "No explanation needed."
The forward's kneeling was similar to a gesture made by former NFL quarterback Colin Kaepernick, who in 2016 began kneeling during the U.S. national anthem to protest police brutality.
Thuram's father Lilian, a retired professional footballer and a 1998 World Cup-winner with France, is an anti-racism activist and UNICEF ambassador.
On Saturday, U.S. international and Schalke midfielder Weston McKennie also displayed his support for Floyd, wearing an armband with the message: "Justice for George." On Sunday, McKennie posted his support for Thuram on Instagram.
Thuram followed up his first goal with a second after 59 minutes, giving Gladbach a 3-1 lead against Union Berlin after the capital side had equalised just after half-time.
After the game, Thuram led celebrations for teammate Mamadou Doucoure, who made his first-team debut four years after signing for the club. Doucoure has suffered several injuries that have prevented him from appearing for the club since he signed in 2016.