Yuliana Samboni's body - which showed signs of torture - was found in a luxury apartment in the city. It's believed she had been suffocated.
The suspect, who has been detained by the police, is from a wealthy family.
The killing has ignited public anger about child sex abuse as well as over the country's deep social divide.
President Juan Manuel Santos has condemned the killing.
Yuliana Samboni had been playing outside her family home in a working class neighbourhood of Bogota when she was snatched from the street by a man in a grey van.
