Josefowicz was born in Missisauga, Ontario, Canada. When she was a young child her family moved to Los Angeles, California where she started studying the violin at the age of three and a half using the Suzuki method. Her father, physicist Jack Josefowicz, and mother, biologist Wendy Josefowicz, learned with her. Beginning lessons on the violin at age 3, at age five she started formal lessons with Idel Low. At seven she began studies with the distinguished violin teacher Robert Lipsett at The Colburn School. Leila's parents, valuing a well-rounded education, believed that both Leila and her brother Steven stay in the public school system. Jack and Wendy rejected home schooling, and Leila attended public middle and high school despite a very full schedule of music activities.
When Leila was 13 the Josefowiczes moved to Philadelphia so she could attend the prestigious Curtis Institute of Music, where she studied with Jaime Laredo, Jascha Brodsky, Felix Galimir and Joseph Gingold. Leila also attended the Julia R. Masterman School in Philadelphia while at Curtis, completing a bachelor of music degree and her high school diploma in the same year.
While still in her teens, Josefowicz played with symphony orchestras in Europe, Asia and North America, including Philadelphia, Cleveland, Los Angeles, Houston, Chicago, Boston, Montreal and Toronto.
Josefowicz made her Carnegie Hall debut in 1994 performing the Tchaikovsky Concerto with Sir Neville Marriner and the Academy of St. Martin in the Fields. The same year she signed an exclusive recording contract with Philips Classics, recording the Tchaikovsky and Sibelius concertos. Other recordings followed on Warner Classics, Nonesuch Records and Deutsche Grammophon labels that include masterworks for solo violin, recital repertoire and the concertos of Romantic and modern composers.
Josefowicz has kept a busy international schedule as a soloist, performing regularly around the world including North and South America, Europe, Japan, China, New Zealand and Australia. She has a strong interest in jazz, improvisation, and new music.
Josefowicz is acclaimed for championing new compositions, including the works of John Adams, Oliver Knussen and Thomas Adès. In 2008-09, she performed the world premieres of concertos written for her by Esa-Pekka Salonen with the Los Angeles Philharmonic (April 2009); Steven Mackey with the St. Louis Symphony (October 2008); and Colin Matthews with the City of Birmingham Symphony Orchestra (September 2009). More recently she performed the world premiere of the concerto Scheherazade.2 written for Josefowicz by John Adams, which she performed with the New York Philharmonic (March 2015). Performing in the world's major concert halls, Josefowicz continues to play traditional masterworks and champions contemporary compositions, exposing audiences around the world to the aforementioned new violin concertos, with ensembles including the Chicago Symphony Orchestra (Salonen), New York City Ballet Orchestra (Salonen), San Francisco Symphony (Adams and Salonen), St. Louis Symphony Orchestra (Adès), Finnish Radio Symphony Orchestra (Matthews), New World Symphony (Adès), Royal Scottish National Orchestra (Knussen), Los Angeles Philharmonic Orchestra (Mackey), Cleveland Orchestra (Adams), Royal Concertgebouw Orchestra (Adès), Minnesota Orchestra (Vänskä), and Atlanta Symphony Orchestra (Adès).
Josefowicz's concert tours take her to all corners of the world. Some of her recent and upcoming engagements in Europe also include appearances with the Leipzig Gewandhaus Orchestra, the London Philharmonic Orchestra, Munich and Czech Philharmonics, and the London Symphony; performances of the new Salonen concerto in Paris, Stockholm, Lisbon and Ferrara, Italy with the composer on the podium; and a fifth appearance at the London Proms.
Josefowicz received an Avery Fisher Career Grant in 1994. In 2007, she was named a USA Cummings Fellow, United States Artists. For her advocacy of new contemporary works for the violin, Josefowicz was named a 2008 MacArthur Fellow.