Gordon was diagnosed with a dislocated ankle and a fractured tibia, according to Rachel Nichols of ESPN.
The wing's debut with the Celtics only lasted five-plus minutes before he was taken off the court on a stretcher.
Love was also one of the players who showed their respect to Hayward in the locker room during the game, per NBA Central. Cavaliers teammates LeBron James, Dwyane Wade and Isaiah Thomas also reportedly visited the injured player.
Hayward was expected to be a leader on the Celtics this season after signing a four-year deal worth $128 million in the offseason. He is coming off his first career All-Star appearance after seven seasons with the Utah Jazz and has become more of a household name around the NBA.
Bleacher Report's Dan Favale listed him as the No. 14 overall player in the league for the upcoming year.
As Love indicated, an extended absence would not only hurt Boston's chances at contending but also take away one of the NBA's biggest stars.