Costa is currently plying his trade in Major League Soccer with the Galaxy, having signed for the team on loan from Gremio as a designated player.
The warrant was issued by the 8th Family Court of Porte Alegre, Brazil on Friday, May 26 and means Costa will be arrested if he returns to his homeland, as reported by GZH.
Costa's lawyer, Sergio Queiroz, has said the player is looking to appeal the decision so that "justice is done."
The 31-year-old has been in the United States since signing for LA Galaxy in February 2022 but has only made four appearances this season and was sent off in the 3-0 defeat to Houston.
Costa returned to Gremio in 2021 after a decade in Europe where he played and won league titles with Shakhtar Donetsk, Bayern Munich and Juventus.
