Kožená was born in Brno in Moravia. Both her parents had come originally from Bohemia, to the west. She was born one of the two daughters of a mathematician father and a biologist mother. Her father died when she was eleven. As a child she sang in :cs:Kantiléna |Kantiléna, the Children's and Youth Choir headed up by :cs:Ivan Sedláček|Ivan Sedláček and attached to the Brno Philharmonic Orchestra. It was, however, as a professional pianist that she planned to make her career until 1987 when a sports accident at school caused her to suffer a "broken hand": this led her to focus on training for a singing career. From 1987 to 1991 she studied voice at Brno Conservatory with Neva Megová and Jiří Peša, and from 1991 to 1995 she was a student of Eva Blahová at Bratislava Drama College where she graduated in 1995. In 1995, she was a prize winner at the InternationalMozart Competition. From 1996–97, she was a member of the Vienna Volksoper.
Her operatic engagements have included several notable debuts: at the Théâtre du Châtelet in Paris as Orfeo in Gluck's Orphée, conducted by John Eliot Gardiner; at the Vienna Festival as Nerone in Monteverdi's L'incoronazione di Poppea, conducted by Minkowski; at the Edinburgh Festival as Sesto in Mozart's La clemenza di Tito; at the Leipzig Opera as Mélisande in Debussy's Pelléas et Mélisande, conducted by Minkowski; at the Aix-en-Provence Festival as Cherubino in Mozart's Le nozze di Figaro; at the Dutch National Opera as Cleopatra in Handel's Giulio Cesare; and at the Salzburg Festival as Zerlina in Mozart's Don Giovanni under Nicolaus Harnoncourt. She sang the centenary performance of Pelléas et Mélisande at the Opéra-Comique in Paris under Minkowski and most recently Cleopatra in Giulio Cesare under Minkowski. Recent engagements include the roles of Idamante in Mozart's Idomeneo at the Glyndebourne and Salzburg Festivals, Cherubino for both the Bavarian State Opera in Munich and the Metropolitan Opera in New York, Dorabella in Mozart's Cosi fan tutte and her return to the Metropolitan Opera as Varvara and Dorabella. She sings Zerlina with the Metropolitan Opera in Japan, returns to the Salzburg Festival for Idamante and to the Théâtre des Champs-Elysées for Melisande.
Kožená has been married twice. Her first marriage was to the French baritone Vincent le Texier. The marriage ended in divorce after she began a relationship with Sir Simon Rattle. Kožená and Rattle married in 2008 in Brno. The couple have three children, Jonáš, Miloš, and Anežka, born on 21 June 2014.