At the age of 14 he attended a modest night school of drawing in La Boca while working during day on the family's coal-yard. When he became 17 years old he joined the Pezzini Stiatessi Conservatory, where he stayed until 1920.
By the 1920s Marcelo T. de Alvear and his wife were very fond of Quinquela Martín's works, and this admiration led to a lasting friendship. In 1922, Quinquela Martín was assigned as chancellor of the Argentine Madrid Consulate in Spain. On April, 1923 he exhibited at the Círculo de Bellas Artes of Madrid. Two of his works were acquired by the institution (Buque en reparación and Efecto de Sol), while another two were acquired by the Museum of Modern Art of Madrid. In 1925 he set sail for France because—in his own words—"My trip to France is owed to President Alvear, who liked my works and wanted them to be judged by Paris". The Museum of Luxembourg acquired Tormenta en el astillero.
On 1927 he left for New York, where he put part of his work on display at the Anderson Galleries. Accounts say two paintings were bought by "Mr. Havemeyer", who donated them to the Metropolitan Museum of New York. After this exhibition he made several others under sculptor Georgette Blandi's tutelage. Before returning to Buenos Aires, he was invited to Havana by Conde Ribero to exhibit there.
On 1929, on a trip to Italy, he made an exhibition at the Palazzo delle Esposizioni in Rome. The Museum of Modern Art of Rome acquired several paintings which were chosen by Benito Mussolini during the display. Quinquela Martín made his last trip in 1930, to London, where he exhibited at the Burlington Gallery. Several British museums acquired his paintings, including the Museum of Arts of London, Museum of Birmingham, Sheffield, Swansea, Cardiff, New Zealand and St. James's Palace.