Humphries attended Hopkins High School. In 2002 he led them to a 25-2 record and its first state championship in 49 years. In 2003 he was named a 2003 McDonald?s All-American and was named Second Team All-USA by USA Today. He was also named to the Super 25 Basketball Team by USA Today, was named Mr. Basketball in the state of Minnesota and state player of the year by the Minneapolis Star Tribune and College Basketball News. He was one of 10 finalists for the 2003 Naismith Prep Player of the Year Award. He averaged a double-double in his final three seasons, with 25.7 points, 11.4 rebounds and 5.0 assists as a senior.
Humphries verbally committed to Duke University, but later reconsidered and attended the University of Minnesota and was named 2004 Big Ten Freshman of the Year and was also named to the All-Big Ten First Team by the media and coaches. He was named Honorable Mention All-America by the Associated Press and by Rivals.com. He was the first freshman to lead the Big Ten in scoring and rebounding in the same season. He scored in double figures in all 29 games, with 16 point/rebound double-doubles on the season for Minnesota. He averaged 21.7 points and 10.1 rebounds (both tops in the Big Ten), while shooting .444 percent from the field and .742 from the line. In February 18, 2004 he set a school record with 36 points at Indiana. He also set a school record for most points by a freshman for a season with 629. He became the first Big Ten freshman to be named conference Player of the Week in two of the first three weeks of the season.
Humphries was drafted by the Jazz in 2004 as the 14th pick. In April 20, 2005 he scored 12 points with a season-high 12 rebounds in the season finale at Golden State for his first career double-double.