The German official was arrested in the Ipanema neighborhood of Rio de Janeiro.
He placed eighth in the 2016 Olympic Games in Rio de Janeiro.
Bishop Tomé Ferreira da Silva gave Pope Francis his resignation after images circulated online of the bishop seminude during a video call with another man.
Eduardo Leite is the governor of the southern state of Rio do Sul.
President Jair Bolsonaro has exacerbated the anti-LGBTQ+ climate in Brazil, activists say.