John William Brown (born December 28, 1913, in Athens, Ohio; died October 29, 1993, in Medina, Ohio) was a Republican politician from Ohio. He briefly served as the 58th Governor of Ohio from January 3, 1957 to January 14, 1957 and served as lieutenant governor of Ohio in two separate tenures.

Brown served as mayor of Medina from 1950 to 1953. In 1952, he unseated the incumbent lieutenant governor, Democrat George D. Nye and took office as lieutenant governor in 1953. (At the time, the office of lieutenant governor was elected separately from the office of Governor of Ohio). Brown defeated Nye again in 1954 to win a second two-year term.

In January 1957, during Brown's second term as lieutenant governor, Frank Lausche, the Democratic governor of Ohio, resigned in order to take a seat in the United States Senate, which he had won in the 1956 election. Brown, thus, was elevated to the office of governor. Lausche's successor, C. William O'Neill, had already been elected; however, at the time, the U.S. Senate term began on January 3, but the Ohio gubernatorial term did not end until the 14th.

Into the breach stepped the outgoing lieutenant governor. Brown took his eleven-day-long governship very seriously. He moved into the governor's mansion, summoned the General Assembly to hear his state of the state address, demanded and received the governor's salary for the eleven days, and deposited a few boxes of gubernatorial papers with the Ohio Historical Society . All this irritated the governor-elect, C. William O'Neill, greatly.

In 1958, Brown was elected to the Ohio House of Representatives, where he served from 1959-1960. He won election to the Lieutenant Governorship again in 1962, and served another three terms (by this time, the lieutenant governor's term had been extended to four years), from 1963-1975. In 1974, Brown lost his bid for another term to Richard F. Celeste.