The river originates in the Eastern Hills of the Colombian capital Bogotá and flows westward through the city into the Bogotá River.

Fucha is derived from Muysccubun, the indigenous language of the Muisca, who inhabited the Bogotá savanna before the Spanish conquest and means "her" or "female".

[1] The Fucha River originates in the locality San Cristóbal in the Eastern Hills of Bogotá and is named in its upper course Quebrada Manzanares, San Cristóbal, Arzobispo and San Francisco River.

It flows north from the Tunjuelo River westward and respectively forms the boundary between the localities Rafael Uribe Uribe (south) and Antonio Nariño (north) and Tunjuelito and Ciudad Bolivar (south) and Kennedy (north) of the Colombian capital and is canalised between the Carrera Séptima and the Avenida Boyacá.

[2] Four of the fifteen protected wetlands of Bogotá are located in the Fucha River basin.