Jonas Junius, who is competing in the light welterweight division, allegedly grabbed the maid and tried to kiss her. He is also suspected of offering the victim money to sleep with him, police said in a statement.
The maid reported the incident to the police.
The Games' organisers confirmed the incident but said it was in the hands of police.
"Brazilian law needs to be respected," said Rio 2016 spokesman Mario Andrada.
"What we need to ensure is that all the legal procedures are being followed and we are assured that they have been."
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Last week another boxer, Morocco's Hassan Saada, was arrested on suspicion of sexually assaulting two room maids at the Olympic Village.
