The arrest came as some 70 military police fanned out across a slum west of Rio de Janeiro in a huge operation to apprehend those suspected of taking part in the assault that has shocked Brazil.
The detained suspect, who was not identified, was being interrogated, said police, who vowed to bring the other alleged attackers to justice.
Social media networks erupted with outrage over the footage posted on Wednesday featuring the girl naked on a bed and the apparent attackers bragging that she had been raped by more than 30 men.
"Those who committed this heinous crime will be found, will be imprisoned and condemned," Justice Minister Alexandre de Morais told a news conference in Rio Friday night.
Brazil's acting president Michel Temer said: "It is absurd that in the 21st century we should have to live with barbaric crimes such as this."
The video has horrified a country not unused to violent crime.
The UN women's rights agency condemned the case along with another recent alleged gang-rape of a 17-year-old girl in the northeastern state of Piaui.
"They were violently attacked in a context of illegal drug use."
Hundreds of demonstrators gathered in downtown Rio yesterday night waving signs saying "Machismo Kills." and "No means no."
In Sao Paulo, protesters erected a mural with messages including "My body is not yours," and "I like to wear necklines, that's not an invitation to rape me.