Ludwig as 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 the Aachen Opera during Herbert von Karajan's period as conductor. Ludwig's first voice teacher was her mother.
Ludwig made her debut in 1946 at the age of 18 as Orlovsky in Die Fledermaus at Frankfurt, where she sang until 1952. She was a member of the Darmstadt Oper from 1952 to 1954, then sang 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 in 1962 and performed with the company for more than thirty years. In 1954, Ludwig made her debut at the Salzburg Festival as Cherubino and appeared there regularly until 1981. Ludwig made her debut as Brangäne at the Bayreuth Festival in 1966.
Ludwig made her American debut at the Lyric Opera of Chicago as Dorabella in 1959. That same year, she made her debut at the Metropolitan Opera in as Cherubino, and subsequently returned there regularly until 1990. Ludwig first appeared at the Royal Opera House, Covent Garden in 1969 as Amneris in Aida.
As Ludwig's voice matured, she expanded her repertoire from lyric and spinto mezzo-roles to dramatic roles. Her vast repertory eventually grew to encompass Carmen, the Marschallin, Ulrica (Un Ballo in Maschera), Beethoven's Leonore, Monteverdi's Octavia, Dido in Les Troyens, Kundry, Klytemnestra. and contemporary roles by von Einem and Orff. She also ventured briefly into the soprano repertory with performances of Verdi's Lady Macbeth and Strauss's Dyer's Wife.
In addition to her opera performances, Ludwig regularly gave recitals of Lieder and a solist 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.
From 1957 to 1970, Ludwig was married to the bass-baritone Walter Berry; the couple performed together frequently. In 1972, she married the French stage-manager Jean-Emile Deiber.
In 1993-94, 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, "...und ich wäre so gern Primadonna geworden".