Joseph West Molyneaux (December 12, 1863 – January 24, 1940) was a United States federal judge.
Born in Bellevue, Kentucky, Molyneaux received an LL.B. from the University of Cincinnati College of Law in 1882. He was in private practice in Minneapolis, Minnesota from 1884 to 1913. He was a judge on the Minneapolis District Court, Minnesota from 1913 to 1925.
On March 18, 1925, Molyneaux was nominated by President Calvin Coolidge to a new seat on the United States District Court for the District of Minnesota created by 43 Stat. 1098. He was confirmed by the United States Senate on March 18, 1925, and received his commission the same day. He assumed senior status on February 28, 1937. Molyneaux served in that capacity until his death, in 1940.