Thibaud was born in Bordeaux and studied the violin first with his father before entering the Paris Conservatoire at the age of thirteen. In 1896 he jointly won the conservatoire's violin prize with Pierre Monteux (who later became a famous conductor). He was injured while fighting in World War I, after which he had to rebuild his technique. In 1943 he established the Marguerite Long-Jacques Thibaud International Competition, a competition for violinists and pianists with Marguerite Long.
As well as a soloist, Thibaud was noted for his performances of chamber music, particularly as part of a piano trio with the pianist Alfred Cortot and cellist Pablo Casals. He was a friend of Eugène Ysaÿe who dedicated his second sonata for solo violin to him.
Thibaud was killed in an air crash on Mont Cemet. His Stradivarius violin was also destroyed.