Steven Matz was born on May 29, 1991, in Stony Brook, New York, the second child of Ron and Lori Matz. He has an older brother, Jonathan, and a younger sister, Jillian. Ron Matz coached a travel baseball team, and was a service manager at a Jeep dealership in West Islip, New York. Lori was an administrative employee at Comsewogue High School in Port Jefferson Station, New York. Matz and his family, as far back as his grandparents, were fans of the New York Mets. As a child, Matz attended the Nassakeag Elementary School in the Three Village Central School District.
Matz first started playing baseball in the Three Village Little League when he was 8 years old. By age 10, Matz began receiving pitching lessons from former Major League Baseball (MLB) pitcher Neal Heaton. He attended Ward Melville High School in East Setauket, New York, where he pitched and played first base for the school's baseball team. He played varsity since his freshman year, during which time his fastball averaged 90 miles per hour. Matz first drew attention from scouts in the New York Mets organization during a baseball showcase tournament in 2008, and their interest in him continued to grow in subsequent years. MLB scouts began attending his starts regularly during his senior season.
Matz enjoyed a high school rivalry with Marcus Stroman, a friend and future New York Mets teammate, who was pitcher for the nearby Patchogue-Medford High School. Matz and Stroman were teammates on the same elite travel team, the Paveco Storm, for several years in junior high and high school. The two were roommates during the Area Code Games and pitched against each other several times in high school, including a notable game on April 16, 2009, which was attended by more than 50 scouts from every MLB team, and is considered one of the best games in the history of Long Island high school baseball. Matz struck out 12 and allowed one hit, leading his team to a 1–0 victory, while Stroman struck out 14 and allowed three hits, and both pitchers threw complete games. Mets scout Larry Izzo later called it "one of the best duels I've ever seen".
Matz posted a 6–1 win–loss record in his senior season, allowing two earned runs and 14 hits in 54 innings, with 74 strikeouts, and a 0.47 earned run average (ERA), helping Ward Melville win its first league title in 34 years. He also had a .408 batting average with nine doubles, six home runs, and 34 RBIs. Matz was named Newsday's Long Island Player of the Year, and won the Yastrzemski Award as the best high school ballplayer in Suffolk County in his senior year. Forty different NCAA Division I schools attempted to recruit Matz to their college teams.