Early in the first period, Horton crossed the red line and made a pass when Rome delivered the hit well after the pass was made.
After lying motionless on the ice for several minutes, Horton was taken off on the stretcher. Rome was assessed five-minute major for interference and a 10-minute game misconduct.
A story in the Sporting News reported Tuesday that the Rome camp was discussing an appeal.
"I'm looking at it, yes," Rome's agent Jarrett Bousquet told Sporting News. "I'm just talking to Aaron and the (players association) right now. I'm not saying we're even going to do it. It's something, for sure, you have to review."
Should Rome decide to appeal the suspension, he would deal with NHL Commissioner Gary Bettman, who handles all appeals directly.
Horton was taken to hospital, but was alert and able to move all his extremities. Earlier today, Horton was released from hospital but he will miss the rest of the series with a severe concussion.
"Two factors were considered in reaching this decision," said NHL senior vice president of hockey operations Mike Murphy in a statement. "The hit by Rome was clearly beyond what is acceptable in terms of how late it was delivered after Horton had released the puck and it caused a significant injury."
"This has nothing to do with the stage, it's the play," Murphy added. "We looked at the injury and talked to Boston's medical people and it doesn't look good for Nathan to play in this series. This is not about what's happened in the past. This is my standard."
"I think it's important for our whole league to protect our players from those kind of hits," said Bruins head coach Claude Julien. "Again, I support them. Whether you agree or not, you support them. I support them with the Burrows decision and I'm supporting them with this one, as well."
This was Rome's second game misconduct of the Stanley Cup playoffs, with the last one coming in the Western Conference Final series against the San Jose Sharks. Rome offered his thoughts in a statement released after the suspension was handed down.
"I want to express my concern for Nathan's well being and wish him a quick and full recovery," said Rome. "I try to play this game honestly and with integrity. As someone who has experienced this type of injury, I am well aware of its serious nature and have no desire for another player to experience it. I will not take away my teammates' focus on the task at hand and intend to speak at an appropriate time in future."
Bousquet told Sporting News that Rome has tried to contact Horton via text and phone call, but has not yet heard back.
Game 4 of the Stanley Cup Final is scheduled for Wednesday night in Boston.