After starting her career in pharmacy, she went on to study radioactivity at the Sorbonne and work in Marie Curies laboratory from 1907 to 1912. At the Curie Institute, Gleditsch performed a technique called fractional crystallisations', which purified radium. The work, which was highly specialized and few could complete, allowed her laboratory fees to be waived. She spent five years of analysis with Curie and returned even after leaving the lab to supervise experiments. In 1911, she received a "Licenciée en sciences degree" from the Sorbonne and was awarded a teaching post at University of Oslo where she worked with Margot Dorenfeldt. After working one year, Gleditsch won the first scholarship ever given to a woman from the American-Scandinavian Association to study in the United States, but was turned down by both of the schools at which she applied.
She went anyway and despite having been rejected was able to work at the laboratory of Bertram Boltwood at Yale University, where she measured the half-life of radium, creating a standard measurement that was used for many years. One of the scientists who had originally turned her away from Yale, co-authored two articles with her and in June 1914, Smith College awarded her an honorary doctorate for her work. In 1913–14, she returned to the University of Oslo and became the second woman to be elected to Oslo's Academy of Science in 1917. During the 1920s, Gleditsch made several trips to France to assist Curie, as well as a trip to Cornwall to investigate a mine located there.
In 1919, Gleditsch co-founded the Norwegian Women Academics' Association, to focus on development of science and the conditions under which women scientists worked. She also believed that cooperation of scientists would foster peace. She served as president of the organization from 1924 to 1928. Joining the International Federation of University Women in 1920, she served as its President from 1926 to 1929,  working to provide scholarships to enable women to study abroad. In 1929, she made a trip to the United States traveling from New York to California with the intention of promoting scholarships for women.
Though her appointment as professor at Oslo in 1929 caused controversy, she successfully started a radioactivity research group there. Throughout the 1930s, she continued to produce articles in English, French, German and Norwegian. She also hosted a series of radio shows to promote and popularize scientific study. In the 1930s she directed, a laboratory doing radiochemistry in Norway, which was used as an underground laboratory by scientists fleeing from the Nazi regime. In 1939, she was appointed to the International committee on intellectual cooperation, where Marie Curie had also been sitting a few years earlier. When Norway was occupied during the war, she hid scientists and continued using her home for experiments. During a raid on her laboratory in 1943, the women scientists were able to rescue the radioactive minerals, but all of the men were arrested.
She retired from the university in 1946 and began working with UNESCO in their efforts to end illiteracy. In 1949, she was actively involved on the working committee and in 1952 was named to the Norwegian commission working to control use of the atomic bomb. That same year she resigned from UNESCO in protest over the admittance of Spain under Franco's fascist regime as a member. In 1962 at the age of 83, she received an honorary doctorate from the Sorbonne, the first woman to receive such an honor.