Muñoz went to Chaffey High School in Ontario, California. He played college football at the University of Southern California. He also played baseball there, pitching for USC’s national championship team in 1978.
Muñoz was the third overall pick in the 1980 NFL Draft by the Cincinnati Bengals. His selection was viewed as a major risk by many pundits since knee problems limited the 6 ft. 6 in., 280-pound Muñoz to just a combined eight games in his junior and senior seasons, though he did return for USC's 17–16 Rose Bowl win over Ohio State University on New Year's Day 1980.
However, Muñoz became a starter in his rookie season and remained a fixture at left tackle for the Bengals for 13 seasons and is considered one of, if not the greatest, offensive linemen in NFL history. Despite his history of injuries, Muñoz missed just three games during his first 12 seasons. His rigorous workout routine included working out in the weight room he had installed in his home and running three to four miles every day. In addition to his talents as a blocker, Anthony Muñoz was also a capable receiver, notching seven receptions for 18 yards and scoring four touchdowns on tackle-eligible plays, including one in 1984 from rookie quarterback Boomer Esiason against the Cleveland Browns in Cleveland.
Muñoz played both Bengals' Super Bowl appearances, XVI and XXIII, both narrow losses to the San Francisco 49ers.
After missing much of the 1992 season battling knee and shoulder injuries, Muñoz attempted to play a 14th season with the Tampa Bay Buccaneers, but he was released before the season started and decided to retire shortly after.
Muñoz was the Offensive Lineman of the Year in 1981, 1987, and 1988, and was awarded the NFL Players Association Lineman of the Year honors in 1981, 1985, 1988, and 1989. The NFL Alumni Association voted Munoz the Offensive Lineman of the Year four times (1987, 1989–1991).
At the time of his retirement, his Pro Bowl selections were tied with Tom Mack for the most ever by an offensive lineman in league history, and also set the Bengals franchise record as well. In 1994, Muñoz was named to the National Football League 75th Anniversary All-Time Team. In 1999, he was ranked #17 on Sporting News' list of the 100 greatest football players and was the highest-ranked offensive lineman. In 2010, he was ranked #12 on the NFL Network's The Top 100: NFL's Greatest Players list and again was the highest-ranked offensive lineman.
Muñoz appeared in two motion pictures: 1980's Borderline as "Guatemalan" and 1983's The Right Stuff (an Academy Award nominee for Best Picture) as "Gonzalez".
From 1994 to 1995, Muñoz served as a color commentator on Fox Sports' NFL telecasts and has for many years been color commentator for TV broadcasts of Bengals' preseason games.
In 1998, Anthony Muñoz was enshrined in the Pro Football Hall of Fame. He was the first Cincinnati Bengals player to be enshrined. Shortly after receiving the honor, Muñoz's hometown of Ontario, California renamed its Colony Park "Anthony Muñoz Hall of Fame Park". The renaming ceremony was held on June 26, 1998, and was attended by Muñoz, his family, city officials, and Ontario residents. The park, incidentally, is the place where Muñoz met his wife DeDe after a pickup softball game during his youth.
In 2002, the Anthony Muñoz Foundation was created to consolidate Muñoz's charitable activities and encourages area individuals and businesses to "...impact area youth mentally, physically and spiritually". In 2004, Muñoz served on a panel to select the year's recipient of the Walter Payton Award. On November 14, 2012, Allstate dedicated a Hometown Hall of Famers plaque to Muñoz at Chaffey High School. On October 8, 2015, Muñoz would receive the Congressional Hispanic Caucus Institute (CHCI) Medallion of Excellence for his contributions to the Hispanic community.
Muñoz is married to DeDe, whom he met at USC and married during his sophomore year in 1978. They have two children. Son Michael Muñoz followed Anthony by playing offensive lineman at Tennessee where he was an All-American and went undrafted. He starred at Moeller High School in Cincinnati. Daughter Michelle played basketball for legendary coach Pat Summitt for the Tennessee Lady Volunteers and later transferred and played at Ohio State. She led William Mason High School in Mason, Ohio to the Division I 1999-2000 state championship, and she was a two-time Ms. Basketball in Ohio in 1999-2000 and 2000-2001.