Claudia Llosa was born in Lima, studied in Newton College and received a degree in communication studies in the University of Lima. She is the niece of the Peruvian writer Mario Vargas Llosa and the film director Luis Llosa. At the end of the 1990s she moved to Madrid, Spain. From 1998 to 2001 she studied at the film academy Escuela TAI. At the end of her studies she started working on the script for Madeinusa. She moved to Barcelona working in the advertising industry. Madeinusa won the prize for the best unpublished script at the 2003 Havana Film Festival.
In 2009 Llosa finished her second film The Milk of Sorrow (La teta asustada) which was shortlisted for the 59th Berlin International Film Festival. It was the first Peruvian film nominated for the Golden Bear award, and won the main award.
On February 2nd, 2010 Llosa’s The Milk of Sorrow was nominated for the Academy Award in the Best Foreign Film Category.