Neunecker was born in Erbes-Büdesheim. She studied musicology and German studies.
She completed her French horn studies with Erich Penzel at the Hochschule für Musik Köln. In 1978 she started her career at the Opern- und Schauspielhaus Frankfurt as second hornplayer. In 1979 she was appointed principal hornplayer with the Bamberg Symphony, and from 1981 to 1989 she held the same position with the hr-Sinfonieorchester. She has appeared as a soloist with various orchestras worldwide, and is also active as a chamber music player.
In 1986 she won first prize at the Concert Artists Guild international competition in New York.
In 1988 she was appointed professor at the Frankfurt Academy of Music and Performing Arts, and in 2004 she was appointed professor of French horn at the Hochschule für Musik ”Hanns Eisler”.
Volker David Kirchner dedicated his Orfeo for baritone, horn and piano on poems from Rilke’s Sonnets to Orpheus to her, premiered on 6 May 1988 in Karlsruhe with Hermann Becht and Nina Tichman.
György Ligeti dedicated to her his Hamburg Concerto, which she premiered on 20 January 2001 in Hamburg with the Asko Ensemble. She also recorded the work for Teldec‘s Ligeti Project series.
Recordings include works by Britten, Hindemith, Mozart and Richard Strauss and also lesser known repertory, such as horn concertos by Reinhold Glière, Paul Hindemith, Othmar Schoeck, and Vissarion Shebalin; three works for horn and piano by Alexander Glazunov; Poème by Charles Koechlin; and the concerto for violin, horn and orchestra by Ethel Smyth.
She has served on the jury of The Aeolus International Competition for Wind Instruments.