Muñoz made his senior debut on 21 August 2016, starting in a 2–1 away loss against UD San Sebastián de los Reyes. He scored his first goal six days later, his team's third in the 4–1 home win over CDA Navalcarnero.[3]
On 30 March 2017, Muñoz agreed to a two-year contract with La Liga club Athletic Bilbao, which was made effective on 1 July; he was initially assigned to the reserves also in the third division.[4] He played his first competitive match with the main squad on 25 October, coming on as a second-half substitute for Ager Aketxe in a 1–1 draw at SD Formentera in the round of 32 of the Copa del Rey.[5][6]
^"Iñigo Muñoz fitxaketa" [Iñigo Muñoz signing] (in Basque and Spanish). Gernika Club. 15 June 2016. Archived from the original on 13 August 2019. Retrieved 27 October 2017.
^Velasco, Juanma (25 October 2017). "Raúl García evita otro desastre" [Raúl García prevents another disaster]. Marca (in Spanish). Retrieved 27 October 2017.
^Zubieta, Jon (25 October 2017). "Un día grande para Óscar Gil y Muñoz" [A great day for Óscar Gil and Muñoz]. Mundo Deportivo (in Spanish). Retrieved 27 October 2017.
^Sokout, Omid (3 January 2021). "Iñigo Muñoz dice adiós al Castellón" [Iñigo Muñoz says goodbye to Castellón] (in Spanish). Castellón Plaza. Retrieved 21 July 2022.