Juszczyk attended Harvard University, where he played tight end for the Harvard Crimson football team under coach Tim Murphy. He played for the Crimson from 2009–2012. Following his senior season in 2012, he was a unanimous first-team All-Ivy League selection.

The Baltimore Ravens chose Juszczyk in the fourth round (130th overall) of the 2013 NFL Draft. He was the first fullback selected of the three chosen in the 2013 NFL Draft. Juszczyk became the first fullback drafted from Harvard and only the tenth player in school history to be drafted. He was the second highest selection in school history, only behind Isaiah Kacyvenski, who was selected in the fourth round (119th overall) in the 2000 NFL Draft.

On May 2, 2013, the Baltimore Ravens signed Juszczyk to a four-year, $2.46 million contract that includes a signing bonus of $300,574.

The following year, Juszczyk became the Baltimore Ravens’ starting fullback with the release of Vonta Leach in February. He also switched his jersey number from #40 to #44, which he had worn at Harvard and Leach had worn the season before. He earned his first career start in the Raven’s season-opener loss to the Cincinnati Bengals. On September 21, 2014, he caught three passes for a season-high 54 receiving yards and caught his first career touchdown reception during a 23-21 defeat of the Cleveland Browns. His first career reception was a nine-yard touchdown pass from Joe Flacco. In a Week 10 matchup against the Tennessee Titans, Juszczyk caught a season-high three passes for 26 receiving yards during a 21-7 victory. Juszczyk finished the season with 19 receptions for 182 receiving yards and a touchdown while starting 14 games and appearing in all 16 games. He was named a Pro Bowl alternate at Fullback after the 2014 season.

Juszczyk returned as the starting fullback in 2015 after winning the job over Kiero Small in training camp. In the season-opener against the Denver Broncos, he had four catches for 17 receiving yards. On October 11, 2015, Juszczyk caught three passes for 31 receiving yards and caught his first touchdown of the season, on an eight-yard pass from Joe Flacco, as the Ravens lost 33-30 to the Cleveland Browns. During a Week 10 loss to the Jacksonville Jaguars, he made a season-high five receptions for 47 receiving yards. The next game, he caught three passes for ten yards and had his first two career carries for three rushing yards during Baltimore’s 16-13 victory over the St. Louis Rams. On December 27, 2015, Juszczyk caught five passes for a season-high 55 receiving yards as the Ravens defeated the Pittsburgh Steelers 20–17.

Entering the regular season in 2016, Juszczyk was the Baltimore Ravens’ starter at fullback and was one of only 17 full-time fullbacks to play in 2016. On September 11, 2016, in the season opener against the Buffalo Bills, he caught two passes for 22 receiving yards and had one carry for two yards as the Ravens won 13-7. On October 2, 2016, Juszczyk caught a career-high six passes for 56 receiving yards as the Baltimore loss to the Oakland Raiders 28-27. On December 25, 2016, Juszczyk scored his first career rushing touchdown against the Pittsburgh Steelers on Christmas Day. He finished the Ravens’ 27-31 loss to the Steelers with two carries for 15 rushing yards and his first NFL rushing touchdown while catching two passes for 10 receiving yards. The Ravens were eliminated from playoff contention with the loss. On January 20, 2017, it was announced that was elected as an original selection to his first Pro Bowl. Pro Football Focus ranked Juszcyzk as the top fullback for 2016. He played the most snaps of any fullback in 2016, finishing with 465, which was 115 more than any other fullback.

Juszczyk entered free agency for the first time in his career in 2017 and was the top fullback on the market. He received interest and offers from multiple teams, including the Philadelphia Eagles, Cleveland Browns, Buffalo Bills, and the San Francisco 49ers. The Philadelphia Eagles were the top team to possibly land the prized free agent at first, but the Buffalo Bills overtook them as the favorite, as they were looking for a stable replacement for Jerome Felton.

On March 9, 2017, the San Francisco 49ers signed Juszczyk to a four-year, $21 million contract that includes $7 million guaranteed and a signing bonus of $5 million. It was the largest contract for a fullback in NFL history.

In his 49ers debut, Juszczyk had two receptions for 17 yards in the season-opening 23–3 loss to the Carolina Panthers. On December 19, 2017, he was named to his second Pro Bowl.

In the 2018 season opener against the Minnesota Vikings, Juszczyk recorded a 56-yard reception in the 24–16 loss. During Week 3 against the Kansas City Chiefs, he scored his first touchdown of the season on a 35-yard pass from Jimmy Garoppolo.

In the 2019 season, Juszczyk appeared in 12 games and recorded 20 receptions for 239 receiving yards and one receiving touchdown.