Novacek was selected in the sixth round (158th overall) of the 1985 NFL Draft by the St. Louis Cardinals. He was also selected by the Houston Gamblers in the fifth round (69th overall) of the 1985 USFL Draft. As a rookie, he was a wide receiver and played mainly on special teams.
In 1986, he was moved to tight end, but was placed on the injured reserve list on August 19. He was activated on October 17, but was placed again on the injured reserve list on December 10.
In 1987, he began the season as the starter at tight end, until suffering a broken elbow against the New York Giants on October 25. After rookie Rob Awalt had a break-out game against the Philadelphia Eagles, Novacek was placed on the injured reserve list on November 2. He finished the season with 20 receptions for 254 yards and 3 touchdowns, producing just 2 receptions in his first two seasons and only 22 after three years.
In 1988, the Cardinals franchise moved to Phoenix and even though Awalt remained the starter at tight end, Novacek still ranked third on the team with 569 receiving yards and 4 receiving touchdowns. The next year with Gary Hogeboom instead of Neil Lomax as the team's starting quarterback, his production fell to 23 receptions for 225 yards and one touchdown.
In 1990, Joe Bugel was hired as the new head coach, who looked for the tight end position to be either a blocker or perform H-back type functions. Novacek was not seen as a good fit for the new system and was left unprotected—eligible to sign with any team under Plan B free agency.
In 1990, the Dallas Cowboys signed Novacek as a Plan B free agent, arguably the best signing in the history of this program. He was named the starter at tight end, even though the Cowboys also acquired Awalt to compete for the position. He would go on to have a break-out season, becoming one of the league's top receiving tight ends, while registering 59 receptions for 657 yards and 4 touchdowns.
He was a key contributor for the offense in the early 1990s, especially on third downs where he could find the soft spot in the defense. Beginning in 1991, he played in five straight Pro Bowls, while helping the Cowboys make the playoffs each year and winning the Super Bowl three times in four seasons. Although blocking was not his strength, he did a solid job locking up opponents.
In 1992, he was named an All-Pro after leading all tight ends with 68 receptions for 630 receiving yards and 6 touchdowns.
In 1995, he posted his second-highest single-season total for receptions (62) and touchdowns (5), to go along with a career-high in receiving yards (705). He underwent arthroscopic surgery on his right knee to repair a partial tear of his medial meniscus before the last game of the season, but still helped beat the Pittsburgh Steelers in Super Bowl XXX.
In 1996, although he missed the regular season because of a degenerative disc in his back, the Cowboys decided not to put him on injured reserve, in the hope he could be ready for the playoffs. On January 3, 1997, he was placed on the injured reserve list. On July 15, he officially retired from the NFL after his chronic lower-back problems cut short his career.
In his 11 seasons, Novacek recorded 422 receptions for 4,630 yards (ninth in team history) and 30 touchdowns, with most of his production coming from 1990 to 1995. He also came up big in the post-season, ranking third in franchise playoff history in receptions (62), receiving yards (645) and touchdown receptions (6).