Eichner was born to Johann Andreas Eichner (1694–1768), a court musician to the court of Waldeck. His father provided him with his primary musical education. He became widely known as a virtuoso bassoonist throughout Europe as a result. In 1762 he entered into the service of Duke Christian IV of Zweibrücken as a violinst. In 1768, he became the concertmaster of the court orchestra, the Mannheim Orchestra, where he remained until 1772. He was highly respected by his contemporaries, and achieved international recognition as an accomplished composer, bassoonist, and concertmaster during his lifetime. Eichner, however, died young and was quickly forgotten. To musicologists, he is known as a representative of the Mannheim School. His 31 symphonies and 20 concertos comprise the main body of his works, but he also composed chamber music including Six Flute Quartets, Opus 4. In 1772 his compositions were published almost simultaneously in Paris, London, and Amsterdam. Christian Friedrich Daniel Schubart praised Eichner's works in 1784 for their gracious charm and "melting sweetness". His Harp Concerto in D Major, Opus 9 (movements: Allegro, Andante, and Tempo di Minoetto), is performed to this day. His daughter was composer Adelheid Maria Eichner.