Sprouse, one of the stars of the US TV drama, recounted how he was taking part in a peaceful demonstration on Sunday when he was detained by police.
Like many US cities, Santa Monica has seen protests following the death of unarmed African-American George Floyd.
"This is ABSOLUTELY not a narrative about me," Sprouse said on Instagram.
In a lengthy post, he added that his account was not intended to distract from the protesters' cause, adding: "Black Lives Matter."