Horton, ninth on the team in scoring with 32 points in 46 games, has not played since suffering the injury during a January 22 game against the Philadelphia Flyers.
"If he were to be cleared at some point, he would need at least a couple of weeks to get back," Bruins general manager Peter Chiarelli said on the team's website.
"He's quite far off right now ... I know he's skating, but he's having little bouts here and there of post-concussion symptoms."
Horton, 26, missed the final four games of the 2011 Stanley Cup Final with another concussion.
Boston opens their best-of-seven Eastern Conference quarter-final at home on Thursday against the Washington Capitals.