Friderike Klauner, daughter of a civil servant, studied history and German language and literature at the University of Vienna from the winter semester of 1935/36. After four semesters, she switched her major to art history with a minor in history. In July 1941, she submitted her dissertation on the topic of The Living Space in Viennese Biedermeier to Hans Sedlmayr. On 30 October 1941, even before she took the final examination in December 1941, Klauner had begun working on a contract basis at the State Arts and Crafts Museum in Vienna. There she inventoried the objects taken over from the Furniture Collection. On the basis of a decree issued by the Reichsstatthalter (Reich Governor) in April 1943, "non-civil servant staff members" were to be reported to the regional labour office for use elsewhere. Subsequently, from June to September 1943, Klauner was obliged to serve at the St. Florian Historical Institute, which, after the closure of the Augustinian Canons' Monastery in 1941, administered the archives and libraries of the closed monasteries as an institution subordinate to the Reich Governor of the Upper Danube Region. From October 1943 she worked as a research assistant in the library of the musicological institute of the University of Vienna. She had to leave in December 1944 due to a conflict with the director of the institute, Erich Schenk, who did not like her independent way of working.
From June 1945, Friderike Klauner worked on an honorary basis as a research assistant in the Gemäldegalerie (Picture Gallery) of the Kunsthistorisches Museum (KHM). In 1947, prior to her employment at the KHM, the Ministry of the Interior checked Klauner's political views. Apart from her membership in the Bund Deutscher Mädel (League of German Girls) during her studies, there was no political affinity with the NSDAP. Promoted by the director of the Picture Gallery, Ernst Buschbeck, she fulfilled important academic agendas and administrative tasks from 1948 onwards, such as the revision and rearrangement of the collection, inventory control, preparations for exhibitions, salvage and acquisitions. In Buschbeck's absence, she was repeatedly entrusted with the deputy management of the Picture Gallery. In July 1948, for example, she took over the objects from the collections of Alphonse and Louis Rothschild that had been given to the KHM in return for an export permit. She was also involved in the export-related dedication of the painting Cardinal Bessarion by Gentile Bellini from Erich Lederer's collection in 1950. In 1952, Klauner was appointed scientific assistant to the Picture Gallery and was promoted to curator 2nd class in 1954 and 1st class in 1962. In 1967, the Federal Minister of Education appointed her Director of the Picture Gallery. In 1973, the board of collection directors finally elected Friderike Klauner as the first female First Director of the Kunsthistorisches Museum. She held this position in addition to heading the Picture Gallery, and in 1976/77 she also took over the administration of the Collection of Sculpture, Arts and Crafts. Alongside important publications and exhibitions, during her time in office she opened the newly established Secondary Gallery in 1968/1971, the renovated Carriage Museum in Schönbrunn in 1974, the Portrait Gallery on the History of Austria in Ambras Castle in 1976 and the Ephesus Museum in the Neue Burg in 1978. For her achievements, Friderike Klauner received the Österreichisches Ehrenkreuz für Wissenschaft und Kunst 1. Klasse (Austrian Cross of Honour for Science and Art 1st class) in 1977, the Richard Meister Medal of the University of Vienna and the Fürstlich Liechtensteinischer Verdienstorden (Princely Liechtenstein Order of Merit), as well as the Golden Ehrenzeichen für Verdienste um das Land Wien (Golden Decoration of Honour for Services to the State of Vienna) in 1986. In 2004, eleven years after Klauner's death, the Vienna City Council named a lane in Vienna Strebersdorf after her.