He attended the public schools of East Cleveland, the University School in Shaker Heights, Ohio, and the University of Virginia at Charlottesville, Virginia, where he was a member of the Chi Phi Fraternity. He graduated from the Cleveland Law School in 1940, was admitted to the bar the same year and commenced the practice of law in Cleveland, Ohio.
He enlisted in December 1940 as a private in the United States Army and served in the European Theater, G-2 section, Headquarters III Corps, and was discharged as a lieutenant colonel in March 1946. He was awarded a Bronze Star. He was special assistant attorney general of Ohio from 1948 to 1952 and general counsel for the Maritime Administration of Washington, District of Columbia, in 1953 and 1954.
Minshall was elected as a Republican to the Eighty-fourth Congress and to the nine succeeding Congresses and served until his resignation December 31, 1974.
He was not a candidate for reelection in 1974 to the Ninety-fourth Congress. He was a resident of Delray Beach, Florida, until his death on October 15, 1990.
He was a member of the Ohio House of Representatives in 1939 and 1940.