He was born in Versailles, and was initially taught by his father with later lessons from Anton Stamitz. He became one of the foremost violin virtuosi of his day, appearing as a soloist until 1810. After hearing him play the violin in Vienna, Ludwig van Beethoven dedicated his ninth violin sonata (the so-called Kreutzer Sonata, 1803) to him. For a time he was leader of the Paris Opera, and from 1817 conducted there.
He was a violin professor at the Paris Conservatoire from its foundation in 1795 until 1826. He was co-author of the Conservatoire's violin method with Pierre Rode and Pierre Baillot. The three are considered the founding trinity of the French school of violin playing.
Kreutzer died in Geneva.
Kreutzer's compositions include nineteen violin concertos and around forty operas. He is best known today, however, for the 42 études ou caprices (1796), which are still used as pedagogic studies.
Rodolphe Kreutzer was the brother of violinist and composer Jean Nicolas Auguste Kreutzer (1778-1832) and the uncle of the writer on music Léon Charles François Kreutzer (1817-1868).