The young winger played in a career-low 46 games this season, while collecting 17 goals and 15 assists for 32 points.
During last year's Stanley Cup run, Horton had three game-winning goals, including the winners in the Game 7 victories over the Montreal Canadiens and the Tampa Bay Lightning, but missed the final four games of the championship series against the Vancouver Canucks after sustaining a concussion in Game 3.
The defending champions play Game 1 of their first-round series against the Washington Capitals on Thursday night at TD Garden.
Meanwhile, defenseman Adam McQuaid will not be in the lineup for Game 1 as he injured his eye on a hit by the Capitals Jason Chimera on March 29.
The availability of defenseman Johnny Boychuk, who sustained a knee injury when he was hurt on a collision with Pittsburgh Penguins forward Aaron Asham on April 3, will be a game-time decision.