Mr Floyd - a black man who was in handcuffs at the time - died after a white Minneapolis officer ignored bystanders' shouts to get off him and Mr Floyd's cries that he couldn't breathe.
His daughter, Gianna, and her mother Roxie Washington then spoke at a news conference where Ms Washington said: "This is what those officers took [...] Gianna does not have a father."
Speaking about the officers involved in Mr Floyd's arrest, Ms Washington said: "At the end of the day, they get to go home and be with their families."
She added Mr Floyd "will never see her [Gianna] grow up, graduate, he will never walk her down the aisle.
"If there's a problem she's having and she needs her dad, she does not have that anymore.
"I want justice for him because he was good.
"No matter what anybody thinks, he was good.
"And this is the proof that he was a good man."
Events were largely peaceful, despite President Trump's threats to put army on the streets to end the protests.
The family's procedure differs from the official post-mortem as described in a criminal complaint against the officer that said it found nothing "to support a diagnosis of traumatic asphyxia or strangulation".
Derek Chauvin has been charged with third-degree murder and manslaughter and is in custody in a state prison.