"No justice, no peace," she captioned her post, along with the #BlackLivesMatter hashtag.
In a since-deleted comment, one of her followers wondered why protests were still going on after Derek Chauvin and the other three officers involved in Floyd's death had been charged -- saying there was "justice" and asking, "sooooo can we have peace now?"
Turner told them to look at the bigger picture.
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"This isn't just about those 4 cops, this is about Breonna Taylor, this is about Trayvon Martin, this is about Eric Garner, this is about the systemic racism that black people have faced for hundreds and hundreds of years," she replied, pointing out other victims of police brutality.
"This is about changing the system," she continued. "Justice will be done when society reflects our believes that we are all equal. Until then there should be no peace."
In the comments, her "X-Men" costar Alexandra Shipp praised Turner's participation, writing, "So proud of you babe. I know how hard it is to be out in the world right now and your courage speaks VOLUMES. I am constantly in awe of your strength!"
Turner replied, writing, "in awe of YOU mama. I love you."
Derek Chauvin was arrested after video captured him with his knee on Floyd's neck for more than eight minutes during an arrest for allegedly passing a counterfeit $20 bill. Floyd was unresponsive when paramedics arrived and was later pronounced dead.
Chauvin faces 2nd-degree murder and 2nd-degree manslaughter charges.
The three other officers in the arrest -- Thomas Lane, J.A. Keung and Tou Thao -- were charged with aiding and abetting the homicide.