Horszowski was born in Lwów (Lemberg), Austria-Hungary (now Ukraine) and was initially taught by his mother, a pupil of Karol Mikuli (himself a pupil of Frédéric Chopin). He became a pupil of Theodor Leschetizky in Vienna at the age of seven; Leschetizky had studied with Beethoven's pupil Carl Czerny. Leschetizky's sister-in-law, Angele Potocka, referred to Horszowski as "a wunderkind of high order".
In 1901 he gave a performance of Beethoven's Piano Concerto No. 1 in Warsaw and soon after toured Europe and the Americas as a child prodigy. In 1905 the young Horszowski played for Gabriel Fauré and met Camille Saint-Saëns in Nice. In 1911 Horszowski put his performing career on hold in order to devote himself to literature, philosophy and art history in Paris.
While Horszowski's family was of Jewish origin (which made him a fugitive from Europe in the 1930s), he was himself an early convert to Roman Catholicism, and was very devout. As the French critic André Tubeuf has written, "Horszowski was both very Jewish and very Catholic, in both cases as only a Pole could have been."
Horszowski, who was barely five feet tall, had rather small hands, reaching just over one octave; however, Allan Kozinn of The New York Times noted that "he turned this limitation into an asset by focusing on music that was written on a more compact scale and made intellectual rather than physical demands". Horszowski's performances were known for their natural, unforced quality, balancing intellect and emotion. He was frequently praised for his tonal quality, as was common for pupils of Leschetizky.
Having returned to the concert stage with the encouragement of Pablo Casals, he settled in Milan after the First World War, remaining there until he emigrated to the United States during World War II. Following the war, Horszowski frequently gave recitals with artists such as Casals, Alexander Schneider, Joseph Szigeti and the Budapest Quartet. He often appeared at the Prades Festival and the Marlboro Festival.
From 1940 Horszowski lived in the United States, first in New York City and later in Philadelphia. He became an American citizen in 1948. Horszowski performed with the NBC Symphony Orchestra under Toscanini, with whom he was friends, in 1943 and 1953. During the 1954-1955 season, he gave a memorable cycle of Beethoven's entire solo piano works in New York. In 1960 he did the same for Mozart's piano sonatas. His very diverse and extensive repertoire also embraced such composers as Honegger, d'Indy, Martin?, Stravinsky, Szymanowski and Villa-Lobos. In 1979, the pianist recorded several works of Lodovico Giustini on a restored Cristofori pianoforte. These works had been commissioned by Cristofori and are the first known compositions written specifically for the pianoforte.
Horszowski was widely recorded and can be heard on the HMV, Columbia, RCA, Vanguard, Nonesuch, and other labels. His final recordings for Nonesuch were made when he was in his mid to late nineties. He also taught at the Curtis Institute of Music in Philadelphia, where his pupils included Robert Dennison, Julius Eastman, Richard Goode, Dina Koston, Anton Kuerti, Murray Perahia, Peter Serkin, Steven De Groote, Kathryn Selby, Cecile Licad, and Leslie Spotz.
In 1981 the 89-year-old Horszowski married Bice Costa, an Italian pianist. Bice later edited Horszowski's memoirs and a volume of his mother's correspondence about Horszowski's early years. She also discovered and recorded some songs composed by Horszowski on French texts around 1913-1914.
Horszowski's final performance took place in Philadelphia in October 1991. He died in that city a month before his 101st birthday. He gave his final lesson a week before his death.