Born and raised in Matanzas, Cuba, he started playing in organized baseball in 1951. He spent three years playing for the Galveston White Caps, and independent team in the Class B Gulf Coast League. He went to independent Winston-Salem in 1954 before going to the Cleveland organization with Class B Keokuk in 1955. He hit .302 that year, his fifth in Class B, and also played at least one game at each position that season.
When he moved higher, unfortunately, his hitting ability could not keep up. Minor league transaction records from the 1950s are not good, but Izquierdo moved to the Baltimore organization sometime in 1956 and to the Cincinnati organization in 1957. He spent five years in AAA for Cincinnati, playing in Havana and Jersey City. He hit .190 in 998 at-bats over that five-year period.
He retired after the 1961 season to become the bullpen coach for Cleveland, but in 1963, he made a comeback with in the Twins' organization. He hit .297 playing in Class A at age 32. He spent the next two years at AA before once again reaching AAA at age 35 in 1966.
Finally, Izquierdo got his turn. He was hitting .300 in 1967 at AAA Denver when, at age 36, Hank Izquierdo made his major league debut. Used as a reserve, he went 7-for-26 with two doubles and two RBIs in the major leagues.
That would be the extent of his major league career, but not the end of his an interesting story. Izquierdo moved to the Houston organization, playing in AAA through 1969. After the 1968 season, he was driving a taxi in Miami during the off-season and was shot in the stomach during a robbery, nearly dying. His playing career ending in 1969 when he got into a fight with Ted Simmons in a AAA game and swung a bat at him, fortunately missing.
After his playing career, Izquierdo managed in the Mexican League for several years and was a scout for the Twins in the 1980s. At last report, Hank Izquierdo was living in West Palm Beach, Florida.