Pending the appeal, Shaw is suspended through the 2020 season after the NFL found he had bet on league games on multiple occasions this fall.
The appeal had to be filed by 5 p.m. ET Tuesday. If his appeal is denied, Shaw may petition for reinstatement on or after Feb. 15, 2021.
The NFL prohibits all personnel -- players, coaches, owners, officials and league employees -- from wagering on NFL games.
Shaw, who is on injured reserve, has not played during his first season with the Cardinals. He placed at least one of his wagers on Nov. 10 at a Las Vegas sportsbook operated by Caesars Entertainment, multiple gaming industry sources told ESPN.
According to the sources, Shaw bet a three-team parlay on the second-half results of three Week 10 games, including the Cardinals' game at Tampa Bay. On his parlay, Shaw bet against Arizona, backing the Buccaneers to cover the second-half spread against the Cardinals. The Buccaneers failed to cover the second-half spread and the bet, which the sources said was for a few thousand dollars, did not win.
The NFL found no evidence that Shaw used inside information to make his bet or that any game had been compromised.
Shaw, who had a player's card with Caesars, had bet with the company previously, sources said, but not on the NFL until Nov. 10. Immediately after realizing Shaw had bet on the NFL, Caesars contacted the Nevada Gaming Control Board and subsequently the NFL, which launched an investigation.
As first reported by NFL Network and confirmed by ESPN, Shaw met and cooperated with the league office shortly after being notified of the investigation.
The NFL announced Shaw's suspension Friday, with commissioner Roger Goodell emphasizing the league's longstanding policy on sports betting.
"The continued success of the NFL depends directly on each of us doing everything necessary to safeguard the integrity of the game and the reputations of all who participate in the league," Goodell said in a release announcing the suspension. "At the core of this responsibility is the longstanding principle that betting on NFL games, or on any element of a game, puts at risk the integrity of the game, damages public confidence in the NFL, and is forbidden under all circumstances. If you work in the NFL in any capacity, you may not bet on NFL football."
Shaw is represented by Elite Athlete Management. A message left with the agency Tuesday afternoon was not immediately returned.