The suspension was handed down by NFL Commissioner Roger Goodell.
Shaw has not played in 2019 and is on injured reserve.
A statement released by the NFL said the league's investigation found no evidence that any games were compromised or that any inside information was used.
"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. 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," Goodell said. "If you work in the NFL in any capacity, you may not bet on NFL football."
NFL Network Insider Ian Rapoport reported, per sources informed, Shaw went to a Las Vegas casino this fall along with close friends from high school and placed sports bets for the first time based on a misinterpreted understanding of the recent 2018 Supreme Court ruling. He used his own player card and ID.
Shaw flew to New York immediately upon notice to meet with league officials and cooperated fully, Rapoport added.
He is eligible to petition for reinstatement to the league on Feb. 15, 2021 and, pursuant to the NFL-NFLPA Collective Bargaining Agreement, can appeal his suspension by filing notice within three days.