Fischer was born in 1983, in Munich, Germany. She began taking lessons on the violin at age 3 from Helge Thelen, and at 4 began simultaneous studies on the piano with her mother, Viera Fischer, a talented amateur pianist. Young Julia's first advanced studies on the violin came a few years later in Augsburg, at the Leopold Mozart Conservatory; at 9, she began taking instruction at the Munich Academy of Music. Among her most important teachers there has been violin virtuoso Ana Chumachenco. In 1995 Fischer won first prize at the International Yehudi Menuhin Competition, where she also captured a special prize for best performance of a J.S. Bach solo work. The following year, in Lisbon, she won first prize at the Eurovision Competition for Young Instrumentalists, an event broadcast widely throughout Europe. Other important prizes followed as Fischer steadily developed her career as an orchestral soloist and recitalist. She gave regular concerts with major symphony orchestras beginning in the late '90s in both Europe and the United States. 2003 was a pivotal year in her career: in the aforementioned concerts with Lorin Maazel, where she played the Sibelius Violin Concerto with the New York Philharmonic Orchestra at Avery Fisher Hall and the Brahms Double Concerto with the Bavarian Radio Symphony Orchestra and cellist Han-Na Chang at Carnegie Hall, she convincingly established her credentials as one of the most talented violinists of her generation. Thereafter, she made concert tours with many of the world's finest orchestras, including the Academy of St. Martin-in-the-Fields (under Neville Marriner), the Gewandhaus Orchestra (Herbert Blomstedt), and the Royal Philharmonic Orchestra. Her first major recording was a 2001 DVD of Vivaldi's The Four Seasons, with Marriner and the Academy of St. Martin-in-the-Fields. In 2004 she began recording exclusively for PentaTone Classics, her first disc featuring performances of the Prokofiev First Violin Concerto, as well as Khachaturian and Glazunov concertos. Subsequent recordings included a disc of solo works by J.S. Bach, Brahms' chamber music, violin concerto and Double Concerto, and the Mozart Violin Concertos.
Fischer has played many violins on loan, including a Ventapane, a Gagliano, a Testore, a Guarneri del Gesu, and a Stradivarius, though she owns a 1742 Guadagnini, which she purchased in London in 2004, and a 2011 violin by Philipp Augustin, which she has played since 2012.