Meyer began playing the clarinet at an early age. Her first teacher was her father, also a clarinetist. She studied with Otto Hermann in Stuttgart and then with Hans Deinzer at the Hochschule für Musik und Theater, Hannover, along with her brother, clarinetist Wolfgang Meyer, and now-husband, clarinetist Reiner Wehle, who played later in the Munich Philharmonic. She began her career as a member of the Bayerische Rundfunk Symphony Orchestra and the Berlin Philharmonic, where her appointment as one of the orchestra's first female members, caused controversy. Herbert von Karajan, the orchestra's music director, hired Meyer in September 1982, but the players voted against her at the conclusion of her probation period by a vote of 73 to 4. The orchestra insisted the reason was that her tone did not blend with the other members of the section, but other observers, including Karajan, believed that the true reason was her gender. In 1983, after nine months, Meyer left the orchestra to become a full-time solo clarinetist.

Orchestras with which she has performed include the Chicago Symphony Orchestra, the San Francisco Symphony Orchestra, the London Philharmonic Orchestra, the Tokyo NHK Symphony Orchestra, the Melbourne Symphony Orchestra, the Orchestre de la Suisse Romande, the Toronto Symphony Orchestra, the Saint Petersburg Philharmonic Orchestra, the Czech Philharmonic Chamber Orchestra, the Vienna Philharmonic and the Berlin Philharmonic. In addition, she performs regularly with the Radio Symphony Orchestras in Vienna, Basel, Warsaw, Prague, Turin, Budapest, Brussels and Copenhagen and with major orchestras in Spain, Italy, Holland, Japan and Switzerland.

In addition to her work as a soloist, Sabine Meyer is a committed player of chamber music and plays all styles of classical music. She finds great value in continued long-term collaboration with other musicians. She is a member of the Trio di Clarone along with her brother and husband who have recorded many CDs. In late 2006 she undertook a short tour with the Mozart Clarinet Concerto. A particularly notable performance in this tour was at Manchester's Bridgewater Hall with the BBC Philharmonic Orchestra on 5 December. Meyer and her wind quintet have worked as members of the Lucerne Festival Orchestra with Claudio Abbado.

By the 1990s, she had become one of the most notable solo clarinetists, and has released many recordings since then. She records exclusively with the EMI label and can often be heard on classical radio stations. Recent CD releases include a disc of French music for Clarinet and Piano with Oleg Maisenberg, entitled French Recital. A CD of clarinet concertos by Ludwig Spohr and Franz Krommer was released in July 2007, for which she collaborated with her student Julian Bliss.

Meyer and her husband have two children and share a professorship at the Musikhochschule Lübeck, in Schleswig-Holstein, Germany, and live in Lübeck. Her hobbies are cooking, reading and horse-riding. Other "members of the family" include a German shepherd cross, four horses (Sabine Meyer breeds horses) and several cats.