The actor, best known for his role in TV drama Riverdale, said he was with a group of peaceful demonstrators in Santa Monica on Sunday when he was detained by police.
Like many cities across the US, Santa Monica, west of Los Angeles, has been the scene of unrest following the death of unarmed black man Mr Floyd.
Sprouse, 27, revealed his arrest with a lengthy post on social saying he did not want to distract from the protesters' cause, adding "black lives matter".
He said he and other demonstrators were given the option to leave Santa Monica - which was under a 4pm curfew on Sunday - before being arrested with zip ties.
Sprouse said: "It needs to be stated that as a straight white man, and a public figure, the institutional consequences of my detainment are nothing in comparison to others within the movement.”
He shared the message with his 32 million followers on Instagram, alongside a Black Lives Matter banner.
Sprouse, who starred alongside his twin brother Dylan in Disney Channel series The Suite Life of Zack & Cody, said now is a time to "contemplate what it means to stand as an ally".
He added: "I hope others in my position do as well. I noticed that there are cameras that roll within the police cruisers during the entirety of our detainment, hope it helps."
Sprouse said he would speak no further on the arrest, for fear of drawing attention away from the Black Lives Matter movement.
He also shared links to organisations offering help for protesters.