Born in Edmond, Oklahoma, Mornhinweg played high school football in San Jose, California. He led the Oak Grove Eagles to a Central Coast Section championship in 1978 with a 52–7 rout of defending champion St. Francis of Mountain View in the title game at Spartan Stadium.
Following the 1978 championship season as a junior, Mornhinweg was the 1979 Northern California Player of Year as a senior, but the Eagles fell 32–29 in the semifinals to Salinas. For his performance during his time at Oak Grove, the school honored Mornhinweg and inducted him into its hall of fame.
Mornhinweg was a four-year starter at quarterback for the University of Montana in Missoula, where he set 15 passing records. During his junior season in 1982, Mornhinweg led the Griz to its first Big Sky Conference championship in a dozen years.
Through Mornhinweg's performance, Montana inducted him into the Montana Hall of Fame. He earned his bachelor's degree in health and physical education/coaching, then went on to earn a master of science in health and physical education/sports administration from the University of Texas at El Paso. Mornhinweg was not selected in the 1985 NFL Draft.
While a collegiate assistant coach, Mornhinweg became the starting quarterback for the Denver Dynamite in the Arena Football League in 1987. In his first start, he completed 3 of 4 passes for 30 yards and was sacked twice. Soon after, Mornhinweg blew out his knee. His team, however, went on to win the inaugural Arena Bowl I with a 45–16 victory over the Pittsburgh Gladiators.
In 1985, Mornhinweg was the receivers coach at his alma mater, the University of Montana. Between 1988 and 1994, he coached at several universities, including: Northern Arizona (running backs), SE Missouri State (offense), Missouri (tight ends and the offensive line), and again at Northern Arizona (offense).
During 1995 and 1996, Mornhinweg coached with the Green Bay Packers, first as an offensive assistant, then as the quarterbacks coach under head coach Mike Holmgren. From 1997 to 2000, he was offensive coordinator for the San Francisco 49ers, under Steve Mariucci.
In 2001, Mornhinweg became the head coach of the Detroit Lions, taking over a team that saw two head coaches leave in the previous season. He compiled a 5–27 record in two seasons.
His most notable moment as a head coach came in 2002 against the Chicago Bears. The game went into overtime, and the Lions won the ensuing coin toss. However, Mornhinweg felt that having the wind in his favor was more important than getting the ball, despite having Jason Hanson (who hit a then-NCAA record 62-yard field goal in his college days at Washington State University) as his kicker. He elected to kick, rather than receive. As it turned out, the Lions never got the ball; on the Bears' opening drive, Chicago scored a field goal to win the game.
In 2003, he joined the coaching staff of the Philadelphia Eagles. Mornhinweg masterminded the Eagles offense in the final six games of the 2006 season, and into the NFC playoffs. Coach Andy Reid gave Mornhinweg the play-calling responsibilities after the Eagles' disastrous loss to the Indianapolis Colts, 45–21. The Eagles won all six games, employing a more balanced run/pass attack. The wins included a three consecutive December divisional road games, all with a back-up quarterback, Jeff Garcia. It was the only time Reid yielded play-calling responsibilities, a role Mornhinweg continued through the 2012 season, until Reid (and his staff) was fired at the end of that season. Instead of continuing to coach under Reid in Kansas City, Mornhinweg took an offensive coordinator position with the New York Jets in 2013. During his time with the Jets he was the offensive coordinator under Rex Ryan.
On January 21, 2015, Mornhinweg was hired as quarterbacks coach for the Baltimore Ravens. On October 10, 2016, Mornhinweg was promoted from quarterbacks coach to offensive coordinator after Marc Trestman was fired.
During his career as an offensive coordinator, Mornhinweg's offenses have finished 1st, 2nd, 4th, 5th, 9th, 10th, and 12th in total offense, and regularly highly ranked in big plays.
Mornhinweg was at one time the youngest guarterback coach, the youngest offensive coordinator, and the second youngest head coach in the NFL. In all, Mornhinweg has coached a year of high school, ten years in the college ranks, and 20 years in the NFL. Throughout his coaching career, Marty has coached every position on the offensive side of the ball.
Mornhinweg has earned a reputation as top quarterback coach by coaching five different Pro Bowl quarterbacks, Hall of Fame quarterbacks Steve Young and Brett Favre, and quarterback Joe Flacco.
Mornhinweg and his wife, Lindsay, have four children, two daughters and two sons. Madi is a recent graduate of Penn and Molly attends Montana. Skyler was a quarterback in the Ivy League at Columbia (transferred from Florida), and Cade is in high school.