Francis Beattie Brewer (October 8, 1820 – July 29, 1892) was a physician and an American politician and a U.S. Representative from New York.

Born in Keene, New Hampshire, Brewer was the son of Ebenezer and Julia Emerson Brewer and attended the Barnet, Vermont public schools, Newbury (Vermont) Seminary, and Kimball Union Academy in Meriden, New Hampshire.

He served as member of the board of supervisors of Chautauqua County, New York from 1868 to 1879, and was a delegate to the 1872 Republican National Convention.

He was the government director of the Union Pacific Railroad for four years under Presidents Grant and Hayes.

Brewer died in Westfield, Chautauqua County, New York, on July 29, 1892 (age 71 years, 295 days).