Born in Gorliz, Biscay, Undabarrena joined Athletic Bilbao's youth system in 2005, aged 10. He made his senior debuts with farm teamCD Basconia of the Tercera División, in the 2012–13 season. On 28 November 2012, at only 17, Undabarrena made his official debut with the main squad, coming on as a substitute for Igor Martínez in the 77th minute of a 2–0 away win against Hapoel Ironi Kiryat Shmona F.C. in the campaign's UEFA Europa League. Having moved up to play for the reserves in summer 2013, Undabarrena played a prominent role in the team's promotion to the second tier the following season, starting 28 regular league matches and all six of the successful play-offs run. Almost three years after his European bow, Undabarrena made his domestic professional debut on 24 August 2015, starting in a 0–1 home loss against Girona FC. He appeared in almost all of the domestic league matches until 13 February 2016, when he suffered a rupture of the anterior cruciate ligament in his left knee during a fixture against Real Valladolid, requiring a lengthy rehabilitation. Returning to the team eight months later at the end of October, he went on to take part in the majority of the remaining matches during 2016–17 before being withdrawn from the final few games as a precaution to complete his recovery. Undabarrena started the first four fixtures of the next campaign, but then suffered another ACL tear during training, this time to his right knee. In the same period, similar injuries were endured by Aitor Seguín, Undabarrena's long-time teammate which hampered the development of both players and damaged their hopes of moving up to the senior squad; during Undabarrena's lengthy absences, midfielder Mikel Vesga was promoted instead. Despite making a successful return to the B-team with ten appearances and one goal between March and May, Undabarrena was released by Athletic Bilbao on the expiry of his contract on 1 July 2018, ending a 13-year association with the club.
Tenerife
On 3 July 2018, free agent Undaberrena agreed a deal to join second-tier CD Tenerife on a three-year contract.
