Krumpholz was born in Budenice, near Zlonice. He learned music from his father while growing up in Paris; in 1773 he played a successful harp concerto in the Burgtheater in Vienna. After serving three years in Count Esterházy's court orchestra (1773–1776), during which he is said to have taken counterpoint lessons with Joseph Haydn, he embarked on a successful concert tour of Europe. In Paris and Metz, he worked along with manufacturers Jean Henri Naderman, his son François Joseph Naderman, and Sébastien Érard towards improving the construction of the harp. He composed concertos and sonatas for harp and chamber music.
In the end, he drowned himself in the Seine after his wife, a former pupil, Anne-Marie Krumpholtz (1755–1824), also a virtuoso harpist, eloped to London, although the story that this was with pianist Jan Ladislav Dussek is apocryphal.
He was the brother of Wenzel Krumpholz, violinist and mandolin player.
Krumpholz composed 52 sonatas, 6 concertos and many preludes and variations for the harp. He wrote also harp duets, quartets and 4 sonatas for harp, 2 violins, 2 French horns and cello.
Selected works 
- Sonate für Flöte oder Violine und Harfe oder Klavier (published by H. J. Zingel in 1933)
- Sonata B dur pro harfu (Sonata in B-flat major for Harp) (published in 1935 by M. Zunová)
- Concertus in SI b mai ab arpa cum choro musico
- Černušák, Gracián (ed.); Štědroň, Bohumír; Nováček, Zdenko (ed.) (1963). Československý hudební slovník I. A-L (in Czech). Prague: Státní hudební vydavatelství. p. 757. - however, the Czech source mentions, that the written record about his birth in the registers of Budenice or Zlonice from 1739 to 1756 does not exist.
- Sturm, Heribert (1984). Biographisches Lexikon zur Geschichte der böhmischen Länder. Band II, I-M (in German). Munich: R. Oldenburg. p. 322. ISBN 3-486-52551-4. Retrieved 2007-12-18.