John Calvin Brown (January 6, 1827 - August 17, 1889) was governor of Tennessee from 1871 to 1875.

Born in Giles County, Tennessee, Brown was the younger brother of Governor Neill S. Brown. He was admitted to the bar as a young man, opening a law practice in 1848. He was personally opposed to secession, but acquiesced in the decision of his state, fighting in the Civil War. He enlisted as a private in the Confederate infantry but ended up in charge of an entire brigade. He saw action in the battles of Perryville, Missionary Ridge, and Franklin.

His civil rights restored shortly after the war, he was elected to the state legislature in 1869. He was also elected a delegate to the state constitutional convention in 1870 and was elected its president by his peers. This body wrote a document approved by the voters of Tennessee later that year, which stood unamended until 1953, a record for such a document, and still serves as the state's instrument of government today.

He was elected governor in 1871. He was forced to deal with a state government that was deeply indebted, even after all debts incurred in support of the Confederacy were abrograted by the new state constitution and amendment to the United States Constitution. He was able to reduce the state's indebtedness in his two terms (he was re-elected in 1873), and also helped get the first truly effective public school legislation, which called for the establishment of state, county, and city superintended, and the taxes to pay for them, passed by the legislature.

He maintained a lesser public profile after leaving office, and died in 1889, only three years after his brother.