The 1887 Navy Midshipmen football team represented the United States Naval Academy during the 1887 college football season. The team compiled a 3–1 record and outscored its opponents 41 to 22. The Midshipmen shut out their first three opponents, including an 8–0 victory in the seventh installment of the Johns Hopkins–Navy football rivalry. The Johns Hopkins game was played at the Academy grounds in Annapolis, Maryland, and was described by The Sun (New York) as "a veritable slugging match" and "one of the roughest games of football" ever seen there. In the final game of the 1887 season, the Midshipmen lost to the Princeton Tigers "B" team in the final game of the season. The team captain was George Hayward.