Momsen was born in Toledo, Ohio in 1928. He was the son of Rose and Anton Momsen, Sr. He attended Toledo's Libbey High School where he was a star athlete in football, basketball and track. In 1944, he was selected as the first-team center on the Associated Press All-Ohio football team. In announcing the selection, the AP quoted an Ohio coach who said, "Momsen was one of the finest linebackers I have ever seen. He diagnoses plays rapidly, is extremely fast and a terrific tackler." He was also an all-city and all-state basketball player.
University of Michigan
Momsen enrolled at the University of Michigan in 1945. In November 1945, when Michigan's starting center, Harold Watts, was transferred for additional Navy training, Momsen became a starter at center for the 1945 football team. After the 1945 season, Momsen withdrew from school. He entered the military. He also married and had two children. In 1947, he played football for Bob Snyder's Grills in the City Federation football league. In the winter of 1949, Momsen returned to the University of Michigan. Momsen played center and linebacker for the 1949 and 1950 Michigan football teams. Momsen is most remembered for his role in the famed 1950 Snow Bowl game against Ohio State. The game matched Momsen against his younger brother, Robert "Buckeye Bob" Momsen, who was a starter for Ohio State. The game was played in a blizzard, with weather conditions so inclement that Michigan punted on first down for its first two plays from scrimmage, after concluding that the best strategy was to keep the slick ball on the other side of the field and in the hands of Ohio State. The Buckeyes scored when Vic Janowicz kicked a field goal after Robert Momsen recovered a blocked Wolverine kick. With 47 seconds remaining in the first half, Tony Momsen blocked a Janowicz punt and fell on the ball in the end zone for a touchdown. The Wolverines won by a final score of 9-3. Momsen, who scored the game's only touchdown was remembered as "the hero of a brilliant forward wall." Bob Momsen later recalled, "Two brothers got more publicity for playing in a terrible football game than anyone ever deserves." The win over Ohio State sent Michigan to the 1951 Rose Bowl against California. In the lead-up to the Rose Bowl, the Los Angeles Times gave credit to linement Roger Zatkoff and Momsen for leading Michigan's defense: "Zatkoff and Tony Momsen, the other backer-upper in Michigan's usual six-man line defense, are the main reasons why Michigan topped the Big Ten in throttling opponents."
After retiring from football, Momsen worked as a cement contractor and built customized golf clubs. He lived in Sunrise, Florida for the last 25 years of his life. In March 1994, he died at Riverside Methodist Hospital in Columbus, Ohio, due to complications following hip replacement surgery. Three weeks after Momsen's death, Libbey High School announced that Momsen would be included among the initial inductess into the Libbey High School Hall of Fame.