A distinguished German mezzo-soprano, she is known both for her opera performances and her singing of Lieder. Her career spanned from the late 1940s until the early 1990s.
Ludwig was born in Berlin to a musical family; her father, Anton Ludwig, was a tenor and an operatic administrator, her mother, the mezzo-soprano Eugenie Besalla-Ludwig, who sang at the Aachen Opera during Herbert von Karajan's term as conductor there. Ludwig’s first voice teacher was her mother.
Ludwig made her début at the age of 18 as Orlovsky in Die Fledermaus at Frankfurt (1946), where she sang until 1952. She was a member of the Darmstadt Oper from 1952 to 1954, then sang during the 1954–1955 season at the Staatsoper Hannover. She joined the Vienna State Opera in 1955, where she became one of its principal artists and was appointed Kammersängerin (1962); she performed with the company for more than thirty years. Ludwig first appeared at the Salzburg Festival as Cherubino in Le Nozze di Figaro (1954), and returned there regularly until 1981. She made her début at the Bayreuth Festival as Brangäne in Tristan und Isolde (1966).
Ludwig made her first American performance at the Lyric Opera of Chicago as Dorabella in Così fan tutte (1959). That same year, she made her début at the Metropolitan Opera as Cherubino, and returned there regularly until 1990. Ludwig first appeared at the Royal Opera House, Covent Garden, as Amneris in Aida (1969).
As Ludwig's voice matured, she expanded her repertoire from lyric and spinto mezzo-soprano roles to dramatic ones. The repertoire eventually grew to encompass Carmen, Ulrica (Un Ballo in Maschera), Monteverdi's Octavia (L'Incoronazione di Poppea), Dido (Les Troyens), Kundry (Parsifal), Klytemnestra (Elektra) and contemporary roles by von Einem and Orff. She also ventured briefly into the soprano repertoire with performances of Verdi's Lady Macbeth (Macbeth), Strauss's Dyer's Wife (Die Frau ohne Schatten), the Marschallin (Der Rosenkavalier) and Beethoven's Leonore (Fidelio) .
In addition to her opera performances, Ludwig regularly gave recitals of Lieder and as a soloist with orchestras. Her performances of Schubert, Schumann, Brahms, Wolf, Mahler and Strauss are much admired. She also sang Bach and performed and recorded most of his major vocal works.
In 1993–1994, Ludwig gave a series of farewell recitals in many cities and made her farewell appearance at the Met, singing Fricka in Die Walküre.
In 1994, Ludwig published a memoir with Peter Csobádi.