He was born in Solln, near Munich. His parents were Karl T. Fischer, Professor of Physics at the Technical University of Munich (TU), and Valentine née Danzer. He graduated in 1937 with Abitur. Before the completion of two years' compulsory military Service, the Second World War broke out, and he served in Poland, France, and Russia. During a period of study leave, towards the end of 1941 he began to study chemistry at the Technical University of Munich. Following the end of the War, he was released by the Americans in the autumn of 1945 and resumed his studies, graduating in 1949.

Fischer worked on his doctoral thesis as an assistant to Professor Walter Hieber in the Inorganic Chemistry Institute, His thesis was entitled "The Mechanisms of Carbon Monoxide Reactions of Nickel(II) Salts in the Presence of Dithionites and Sulfoxylates". After receiving his doctorate in 1952, he continued his research on the organometallic chemistry of the transition metal and indicated with his lecturer thesis on "The Metal Complexes of Cyclopentadienes and Indenes". that the structure postulated by Pauson and Keally might be wrong. Shortly after he published the structural data of ferrocene, the sandwich structure of the η (pentahapto) compound. He was appointed a lecturer at the TU in 1955 and, in 1957, professor and then, in 1959, C4 professor. In 1964 he took the Chair of Inorganic Chemistry at the TU.

He lectured across the world on metal complexes of cyclopentadienyl, indenyl, arenes, olefins, and metal carbonyls. In the 1960s his group discovered a metal alkylidene and alkylidyne complexes, since referred to as Fischer carbenes and Fischer-carbynes. Overall he published about 450 journal articles and he trained many PhD and postdoctoral students, many of whom went on to noteworthy careers. Among his many foreign lectureships, he was Firestone Lecturer at the University of Wisconsin–Madison (1969), visiting professor at the University of Florida (1971), and Arthur D. Little visiting professor at the Massachusetts Institute of Technology (1973).

In 1964, he was elected a member of the Mathematics/Natural Science section of the Bavarian Academy of Sciences. In 1969 he was appointed a member of the German Academy of Natural Scientists, Leopoldina and in 1972 was given an honorary doctorate by the Faculty of Chemistry and Pharmacy of the University of Munich.

He has received many awards including, in 1973 with Geoffrey Wilkinson, the Nobel Prize in Chemistry for his work on organometallic compounds.

He died on 23 July 2007 in Munich. At the time of his death, Fischer was the oldest living German Nobel laureate. He was succeeded by Manfred Eigen, who shared the Nobel Prize in Chemistry in 1967 and is nine years younger than Fischer was.