He graduated from the Universidad Central de Madrid (present day Complutense University of Madrid) in Physics and Mathematics, earning a doctorate in Physics in 1901 with thesis Sobre la Variación Diurna de la Componente Horizontal del Viento written under the supervision of Santiago Ramón y Cajal.

Along with the review published in 1912 by Esteban Terradas of Max von Laue's book Das Relativitätsprincip, which had appeared the previous year, these works were meant to introduce the special theory of relativity to Spain.

In 1928 he became a member of the French Academy of Sciences, sponsored by physicists Paul Langevin and Maurice de Broglie.

That year he received the greatest recognition of his whole career: at the request of Einstein and Marie Curie, Cabrera was named a member of the 6th Scientific Committee of the Solvay Conference.

In 1929, Cabrera replaced Leonardo Torres Quevedo, who had abandoned his post due to health problems, at the International Bureau of Weights and Measures.In 1931 he was named director of the Universidad Central de Madrid.

In 1933, he participated in the creation of the Summer International University of Santander (now the Universidad Internacional Menéndez Pelayo), being called as its director the following year.

Nevertheless, after the end of the war, the Franco government demanded that he leave the post, even though the position had no representative value with respect to Spain.

In 1944 he began to direct the magazine Ciencia, edited by exiled Spanish scientists; after Cabrera's death the post passed to Ignacio Bolívar.

In this same year, the Spanish Cultural Institution of Buenos Aires published his last work, El magnetismo de la materia.