David H. Armstrong (October 21, 1812 - March 18, 1893) was a United States Senator from Missouri. Born in Nova Scotia, Canada, he attended Maine Wesleyan Seminary and taught school in New Bedford, Massachusetts from 1833 to 1837. He moved to St. Louis, Missouri in 1837, and then to Lebanon, Illinois, where he taught at McKendree College. He returned to Missouri and was principal of the public school at Benton from 1838 to 1847, comptroller of St. Louis from 1847 to 1850, postmaster of St. Louis from 1854 to 1858 and a member of the board of police commissioners from 1873 to 1876.
Armstrong served as a member of the board of freeholders which framed the charter of St. Louis in 1876, and was appointed as a Democrat to the U.S. Senate to fill the vacancy caused by the death of Lewis V. Bogy, serving from from September 29, 1877, to January 26, 1879, when a successor was elected and qualified. Armstrong was not a candidate for reelection in 1879; and in 1893 died in St. Louis. Interment was in Bellefontaine Cemetery.