Zubieta started his playing career in the 1935–36 season at the age of 17. His impressive performances earned him a call-up to the Spain national football team in 1936, making him the youngest player ever to play for Spain at the age of only 17 years and 9 months.
Later in 1936 the Spanish civil war disrupted his playing career. During the conflict he played for the Basque Country national football team. The team undertook a tour of South America and in 1939 Zubieta was signed by Argentine side San Lorenzo de Almagro. Zubieta stayed with the club for 13 seasons, playing 352 games for the club, scoring 29 goals. He occupies 3rd place on the list of San Lorenzo players with most games for the club  During his time at the club, they won the Argentine Primera in 1946 and the Copa Río de La Plata in the same year.
In 1952 Zubieta returned to Spain, joining Deportivo de La Coruña where he played until his retirement in 1956 at the age of 38.