Dozier was born in Norfolk, Virginia. He attended Kempsville High School in Virginia Beach, Virginia, and later attended Penn State University. When D.J. was 12 years old, he played on a youth basketball team for Kempsville and made it to the Virginia Beach city championship game. His team played against the Green Run Suns, who had future NBA Hall of Fame player David Robinson on the team. Kempsville won the game, mainly in part to David Robinson (who was a small forward and not the tallest player on the team nor highest scorer) missing the game due to having come down with the mumps. DJ, who would eventually grow to 6 feet tall, was already 5'9" or 5'10" by 12 years old. With his athleticism, skill and size, Dozier dominated the undefeated Suns and won the city championship.
Dozier, who was 6'0", 202 pounds and who threw and batted right-handed was originally drafted by the Detroit Tigers in the 18th round in 1983 (459th overall). He opted not to sign and decided to go to college, where he would pursue his football career.
In 1990, the New York Mets signed him as an amateur free agent. He spent 1990 and 1991 in the minor leagues, where he showed good speed (he stole 33 bases with St. Lucie in 1990) and also some power (in 1990, he hit 13 home runs with St. Lucie). He played for the Williamsport Bills in 1991.
After spending some time in the minors in 1992, he was called up to the Major Leagues and made his debut on May 6, 1992 at the age of 26. In 25 games, he hit .191 with 4 stolen bases and 19 strikeouts in 47 at-bats. Defensively, he committed 1 error for a fielding percentage of .971.