Katai tea posted twice on its Instagram, the first post asking for the protesters to be killed and the second showing a suspected robber holding a box with the caption “Black Nikes Matter”.
Both posts have since been deleted.
Galaxias said the organization opposes racism.
“Earlier today, the LA Galaxy was informed of a series of racist and violent posts on social media … The LA Galaxy strongly condemned the social media posts and called for their immediate abolition,” the group said.
Alexander Katayi said on Instagram that his wife’s posts were unacceptable.
“These views are not the ones I share and are not tolerated in my family,” he wrote. “This is a mistake of my family and I take full responsibility. I will ensure that my family and I take the necessary steps to learn, understand, listen and support the black community.”
On Friday, the Galaxy issued another statement announcing Katai’s departure, saying the two sides “mutually agreed to separate.”
Katai, 29, was in his first season with the Galaxy after spending two seasons with the Chicago Fire. A resident of Serbia, Katai has played six matches for Serbia, including four in the 2018 World Cup.
Before joining MLS, he has played football clubs in Greece, Serbia and Spain.