Schroeder was born in Washington, D.C., the son of Frances Schroeder, the United States Ambassador to Sweden. His mother was the daughter of William Winston Seaton, who, with his brother-in-law, Joseph Gales, owned and edited the National Intelligencer. Seaton served as the Mayor of Washington, D.C., from 1840 to 1850.
He entered the United States Naval Academy in 1864, which, because of the American Civil War, was in Newport, Rhode Island. After graduating in June 1868 he served with the Pacific Fleet in 1868-69 under Admiral John Rodgers in screw sloop, Benicia, and fought in the Salt River near Seoul, Korea. His sea tours took him to Alaska, Japan, and the Philippines in Saginaw, to the West Indies in Canandaigua, and on a world cruise on Swatara.
Schroeder married Maria Campbell Bache Wainwright on January 16, 1879. Maria Wainwright, born March 14, 1856 in Washington, D.C., came from a family of several American statesmen — she was the great-great-granddaughter of Benjamin Franklin, the great-granddaughter of Treasury Secretary Alexander J. Dallas, the granddaughter of Texas legislator Richard Bache, Jr., a niece of Vice President George Mifflin Dallas, the daughter of naval officer Richard Wainwright, and the sister of Admiral Richard Wainwright. She died in 1925 in Jamestown, Rhode Island.
After specializing in hydrographic duties for 11 years, he spent two years in the Office of Naval Intelligence (ONI) where he helped develop the Driggs-Schroeder rapid-fire gun in partnership with Navy Commander William H. Driggs. He returned to sea in 1890 as the Commanding Officer of Vesuvius. In 1893, he began a three-year tour as ordnance officer for the Washington Navy Yard and as the recorder of the Board of Inspection and Survey; and joined the Board as a member in 1894.
Following his appointment as executive officer of the battleship Massachusetts (BB-2), he participated in the American blockade of Santiago, Cuba, during the Spanish–American War and was advanced three numbers in rank "for eminent and conspicuous conduct in battle" during five engagements between 31 May and 4 July 1898.
He was appointed Naval governor of Guam on 19 July 1900, and there commanded Yosemite and later, Brutus (AC-15). On 1 May 1903, Schroeder became Chief Intelligence Officer of the Navy. He assumed command of Virginia (BB-13) upon her first commissioning on 7 May 1906 and afterwards commanded various divisions in the Atlantic Fleet.
Promoted to Rear Admiral in 1908, he hoisted his flag on Connecticut (BB-18) when he took command of the Atlantic Fleet on 8 March 1909.
Two months later, Schroeder was assigned to the Navy General Board. Schroeder was placed on the retired list on 17 August 1911 and retired to his home in Jamestown, Rhode Island.
Rear Admiral Schroeder was recalled to active duty in 1912 to prepare a new signal book, and again in World War I to serve as Chief Hydrographer and the Navy representative on the United States Geographic Board. He died at the Naval Hospital, Washington, D.C., on 19 October 1922.
In 1942, the destroyer USS Schroeder (DD-501) was named in his honor.