Upon completing his high school education at the Colegio Nuestra del Carmen "Carmelitas", Muñoz was admitted to the Pontifical Catholic University of Peru to study law.

Muñoz ran for mayor of Miraflores at the 2010 Lima municipal elections, where he defeated the incumbent, Manuel Masías.

[5] In 2011, in his capacity as mayor, Muñoz was elected President of the OMAPED National Network Coordinator, a space from which local public policies on accessibility and inclusion for people with disabilities are promoted.

[7] At the conclusion of his first term, Muñoz was successfully re-elected as mayor of Miraflores at the 2014 municipal election, obtaining 41.87% of the popular vote.

[9] On 22 October 2017, Muñoz launched his bid for mayor of Lima as an invited candidate for Popular Action.

[13] On 1 January 2019, Muñoz and his 39 council members were sworn in to their respective positions in the Magic Water Circuit Park.