Alexander W. Monroe (December 29, 1817 – March 16, 1905) was a prominent American lawyer, politician, and military officer in the U.S. states of Virginia and West Virginia. Monroe served as a member of the Virginia House of Delegates (1850–1851 and 1862–1865) and West Virginia House of Delegates (1875–1877 and 1879–1883) representing Hampshire County. He served as the Speaker of the West Virginia House of Delegates during the 1875–1877 legislative session.