Sunnyi Melles is the daughter of the Hungarian émigré music professor and conductor Carl Melles and the Hungarian-Jewish actress Judith Melles, née Rohonczy. Sunnyi Melles grew up with her brother and mother in Basel, Switzerland.

During her school years, Melles received professional ballet, dance, violin, piano, and singing lessons. She appeared on stage at the Basel City Theatre alongside her mother at the age of ten. From 1978 to 1979, she completed her acting training at the Otto Falckenberg School in Munich. From 1980, she performed at the Munich Kammerspiele, where she had her breakthrough, particularly in productions directed by Dieter Dorn; from 1982, she was a member of the Kammerspiele ensemble. There, she portrayed, among other roles, Emilia Galotti in G. E. Lessing's tragedy of the same name and Gretchen in Dieter Dorn's production of Faust. Another highlight was the production of Troilus and Cressida at the Kammerspiele, where she played Cressida. From 1990 to 1993, Melles played Buhlschaft in Jedermann at the Salzburg Festival, opposite Helmuth Lohner. In 2003, she followed her regular director, Dieter Dorn, to the Bavarian State Theatre in Munich. There, she played Elena Andreyevna in Chekhov's Uncle Vanya in a production by Barbara Frey and Isabella in Shakespeare's Measure for Measure, also directed by Dieter Dorn. She was also a member of the ensemble at the Vienna Burgtheater for a time. In 2005, she received the Nestroy Theatre Prize in the category of "Best Actress" for her portrayal of Valerie in Ödön von Horváth's Tales from the Vienna Woods at the Salzburg Festival and the Bavarian State Theatre.

At the age of fourteen, Melles appeared in the feature film Steppenwolf (1974) alongside Max von Sydow. Her breakthrough as a film and television actress came in 1982 with a leading role alongside Otto Sander and Hannelore Elsner in the comedy Wer spinnt denn da, Herr Doktor?. Since 1983, she has regularly appeared in guest roles on the ARD crime series Tatort. She has also played various roles in the crime series Siska. In Bernd Eichinger's 2008 film The Baader Meinhof Complex, directed by Uli Edel, she played Frau Buddenberg. In 2009, she portrayed Barbara Krupp in the ZDF three-part series Krupp – Eine deutsche Familie. In 2012, she took on the role of Marie-Elisabeth von Humboldt, the mother of Wilhelm and Alexander von Humboldt, in Detlev Buck's Measuring the World. In January 2013, she appeared as Ottilie Schadt in the ZDF three-part series Das Adlon. Eine Familiensaga. In 2018, she played the German Empress Auguste Viktoria alongside Sylvester Groth in the docudrama Kaisersturz. In 2019, she participated in the 12th season of the ORF dance show Dancing Stars, where she and her dance partner Florian Vana were the first to be eliminated. That same year, she took on the role of Empress Elisabeth of Austria-Hungary in the "Universum History" docudrama Elisabeth – Kaiserin auf der Flucht (Elisabeth – Empress on the Run).

In the 2023 historical spy thriller Davos 1917 by SRF and ARD, she played the role of Russian informant Olga Belova alongside Dominique Devenport and Jeanette Hain. Her portrayal of the Jewish woman Mimi Zweifler in the six-part ARD miniseries Die Zweiflers earned her the German Television Award for Best Actress in 2024. In 2024, she played the role of Marlene Dietrich in the French Disney+ television series Becoming Karl Lagerfeld.

Melles has also appeared in several children's and youth productions, including the Queen in Václav Vorlíček's The Sea Queen (1998), Frau Magiaro alongside Hans Clarin in Pumuckl and His Circus Adventure (2003), the Queen Mother in the fairy tale film The Clever Peasant Daughter (2009) alongside Maxim Mehmet and Rolf Kanies, and Evelyn Boogle in the crime film The Three Investigators and the Carpathian Hound (2025).

Sunnyi Melles also works as a voice actress in various films and series. In 2005, she voiced the role of Sophie in the Japanese anime film Howl's Moving Castle.