Frederick was the son of Enoch and Rachel (Barnum) Knapp. He was educated in the local schools of New Fairfield, and in Chappaqua, New York. He became the third generation to farm at "Sunny Side Farm" on Barnum Road in New Fairfield. He married Fanny N. Taylor, daughter of Emory and Mary (Cowles) Taylor of Unionvale, Connecticut. Her father was a gunsmith in that town. Frederick was the first Republican elected to the State Legislature in 32 years, and he held that post for many years afterward. He also served as town clerk and tax collector in New Fairifield. In later years, he was employed as Assistant Superintendent of State Buildings, in Hartford, retiring just two years before his death. The last few years of his life were spent in Holnes, New York.
His gravestone reads: Frederick E. Knapp, 1859 - 1937.