In his freshman year, he played in 12 games, notching 6 receptions, 50 receiving yards, and a receiving touchdown. On September 20, 2008, he caught 2 receptions for 15 yards against Notre Dame to help Michigan State win the game, 23–7.

In his sophomore year, he played in 10 games and he recorded 3 receptions for 33 yards and a touchdown. On October 10, 2009, he had 2 receptions for 20 yards against Illinois, in a 24–14 Michigan State victory.

In his senior year, he played in 14 games and recorded 3 receptions, 35 receiving yards, and one receiving touchdown. On September 10, 2011, he had one reception for 8 yards and a touchdown against Florida Atlantic as Michigan State won, 44–0.

On April 29, 2012, the San Francisco 49ers signed Celek as an undrafted free agent after he went unselected in the 2012 NFL Draft. He was signed to a three-year, $1.44 million contract. On September 1, 2012, he earned a spot on the 53-man roster. He began his rookie season as the fourth tight end on the depth chart behind veteran Vernon Davis, Delanie Walker, and Demarcus Dobbs. On October 7, 2012, he made his first career reception against the Buffalo Bills after making his debut against the New York Jets the previous week. He finished his rookie season with four catches for 51 receiving yards and appeared in 13 regular-season contests. The 49ers finished with an 11–4–1 record in his rookie year and he appeared in Super Bowl XLVII, losing to the Baltimore Ravens.

Celek began the 2013 regular season as the third tight end behind veteran Vernon Davis and rookie Vance McDonald. He appeared in the season opener and started the following week, but did not make his first catch of the season until Week 3. During that game he only made one reception for 30 yards in the 49ers’ 7–27 loss to the Indianapolis Colts. Celek finished his second season with two catches for 38 yards in 12 games and one start. On January 5, 2014, he made his first career catch in the postseason after catching a pass from Colin Kaepernick and taking it for six yards during a victory over the Green Bay Packers. The San Francisco 49ers made it to the NFC Championship game that season, but lost to the eventual Super Bowl champions, the Seattle Seahawks, by a score of 23–17.

On March 7, 2015, Celek signed a one-year, $710,000 contract to remain with the 49ers. The contract also included a $25,000 signing bonus.

Celek began his first season under new head coach Jim Tomsula remaining as the third tight end behind both Davis and McDonald. He started the 49ers’ season opener against the Minnesota Vikings, finishing the 20-3 win with a season-high three receptions and 40 receiving yards. On October 11, 2015, against the New York Giants, Celek caught a 5-yard reception from Colin Kaepernick for his first NFL touchdown. On November 8, 2015, he caught two passes for 12 yards and a season-high two touchdowns during a 17–16 victory over the Atlanta Falcons. Celek finished 2015 with a total of 19 receptions, 186 receiving yards, and three touchdown receptions while starting 8 games and appearing in 11.

On February 24, 2016, the 49ers signed Celek to a four-year, $10.20 million contract with $3.50 million guaranteed and a signing bonus of $2.50 million.

In his first season under new head coach Chip Kelly, Celek was named the second tight end behind Vance McDonald to begin the season. In the season-opening 28-0 victory over the Los Angeles Rams, Celek made one reception for 15 yards. On October 2, 2016, he made a career-high five receptions for a career-high 79 receiving yards during the 49ers’ 24-17 loss to the Dallas Cowboys. On November 27, he caught two passes for 19 yards and a 4-yard touchdown pass from Colin Kaepernick for his first touchdown of the season during a 24-31 loss to the Miami Dolphins. Celek finished the season with 29 receptions for 350 receiving yards and three touchdowns in 16 games and six starts.

On August 31, 2019, Celek was placed on reserve/PUP to begin the season. He was activated on November 11, 2019 prior to Week 10. He was placed on injured reserve on December 12, 2019. Without Celek, the 49ers reached Super Bowl LIV, but lost 31-20 to the Kansas City Chiefs.

On February 7, 2020, Celek announced his retirement from the NFL via Instagram.