Leinster was born in Norfolk, Virginia, the son of George B. Jenkins and Mary L. Jenkins. His father was an accountant. Although both parents were born in Virginia, the family lived in Manhattan in 1910, according to the 1910 Federal Census.
He began his career as a freelance writer before World War I; he was two months short of his 20th birthday when his first story, "The Foreigner", appeared in the May 1916 issue of H. L. Mencken's literary magazine The Smart Set. Over the next three years, Leinster published ten more stories in the magazine. During World War I, Leinster served with the Committee of Public Information and the United States Army (1917–1918). During and after the war, he began appearing in pulp magazines like Argosy,
Snappy Stories, and
Breezy Stories. He continued to appear regularly in Argosy into the 1950s. When the pulp magazines began to diversify into particular genres in the 1920s, Leinster followed suit, selling jungle stories to Danger Trails, westerns to West and Cowboy Stories, detective stories to Black Mask and Mystery Stories, horror stories to Weird Tales, and even romance stories to Love Story Magazine under the pen name Louisa Carter Lee.
Leinster's first science fiction story, "The Runaway Skyscraper", appeared in the February 22, 1919 issue of Argosy, and was reprinted in the June 1926 issue of Hugo Gernsback's first science fiction magazine, Amazing Stories. In the 1930s, he published several science fiction stories and serials in Amazing and Astounding Stories (the first issue of Astounding included his story "Tanks"). He continued to appear frequently in other genre pulps such as Detective Fiction Weekly and Smashing Western, as well as Collier's Weekly beginning in 1936 and Esquire starting in 1939.
Leinster was an early writer of parallel universe stories. Four years before Jack Williamson's The Legion of Time came out, Leinster published his "Sidewise in Time" in the June 1934 issue of Astounding. Leinster's vision of extraordinary oscillations in time ('sidewise in time') had a long-term impact on other authors, for example Isaac Asimov's "Living Space", "The Red Queen's Race", and The End of Eternity.
Leinster's 1945 novella "First Contact" is also credited as one of the first (if not the first) instances of a universal translator in science fiction. In 2000, Leinster's heirs sued Paramount Pictures over the film Star Trek: First Contact, claiming that it infringed their trademark in the term. However, the suit was dismissed.
Leinster was one of the few science fiction writers from the 1930s to survive in the John W. Campbell era of higher writing standards, publishing over three dozen stories in Astounding and Analog under Campbell's editorship. The last story by Leinster in Analog was "Quarantine World" in the November 1966 issue, thirty-six years after his appearance in the premier January 1930 issue.
Murray Leinster's 1946 short story "A Logic Named Joe" contains one of the first descriptions of a computer (called a "logic") in fiction. In the story, Leinster was decades ahead of his time in imagining the Internet. He envisioned logics in every home, linked through a distributed system of servers (called "tanks"), to provide communications, entertainment, data access, and commerce; one character says that "logics are civilization."
During World War II, he served in the United States Office of War Information. After the war, when both his name and the pulps had achieved a wider acceptance, he would use either "William Fitzgerald", "Fitzgerald Jenkins" or "Will F. Jenkins" as names on stories when "Leinster" had already sold a piece to a particular issue.
Leinster was so prolific a writer that Groff Conklin, when reviewing Operation: Outer Space in March 1955, noted that it was his fourth novel of 1954 and that another would be reviewed in the next month. Leinster continued publishing in the 1950s and 1960s, appearing in Galaxy Magazine and The Magazine of Fantasy and Science Fiction, as well as The Saturday Evening Post. He won a Hugo Award for his 1956 story "Exploration Team".
Leinster's career also included tie-in fiction based on several science fiction TV series: an episodic 1960 novel, Men into Space, was derived from the series' basic concepts, but Leinster had little knowledge of the series' actual content, and none of the book episodes bear any relationship to the filmed episodes. Men Into Space was followed, seven years later, by two original novels based on The Time Tunnel (1967), and three based on Land of the Giants (1968–69).