Because of difficulties with the immigration office, Maria could not remain in the canton of Zürich, so her foster father found her a place with the Stader family in Romanshorn, where there is also the commemorative Maria-Stader path.

Another native of Budapest, Ilona Durigo, became her vocal teacher in 1935 in Zürich and introduced her to Hermann and Lily Reiff (a student of Franz Liszt).

Stader was a close friend of the Swiss politician Walther Bringolf, as well as of numerous musicians – especially pianist Clara Haskil and the Hungarian conductor Ferenc Fricsay (with whom she became acquainted through Rolf Liebermann).

Stader first achieved fame for her interpretations of Mozart and her collaborations with conductor Ferenc Fricsay on works such as Don Giovanni, Le nozze di Figaro, Die Entführung aus dem Serail, two versions (1954 and 1960) of Exsultate, jubilate and the Great Mass, as well as Verdi's Messa da Requiem.

She won, the Geneva International Music Competition in 1939, but although she "seemed poised for major stardom... her career was delayed by the outbreak of World War II", according to Opera News.

She nearly always performed operatic roles in the recording studio and seldom, if ever, on stage because of her small stature – she was about 1.44 metres (4 ft 9 in) tall.

She stood on the concert podium for the last time in Philharmonic Hall in New York in Mozart's Requiem on December 7, 1969, "still in solid vocal condition".