The hard-hitting Parros, who will be out indefinitely, spent several minutes motionless on the ice, attended to by both teams' medical staffs, before being removed on a stretcher. He was released form the hospital Wednesday morning.
The fight happened early in the third period of Montreal's 4-3 home-opening loss to Toronto.
He thanked his fans on Twitter a few hours later, writing:
Thanks for all the well wishes everyone #classyfollowers
— George Parros (@GeorgeParros) October 2, 2013
"You never want to see a guy get hurt like that," Orr said. "It was a scary situation. I just hope he's all right.
"It happened fast. I slipped, and he came on top of me. The ice isn't going to give."
Parros and Orr have a long history.
The two have fought each other several times, and Orr was injured in a similar fight with Parros two years ago in Toronto. Parros, then with the Anaheim Ducks, landed on Orr, who sustained a concussion and didn't play for the rest of that season.
"Any time you see a guy go down -- no matter what team he's on -- it's pretty scary," Canadiens captain Brian Gionta said. "Hopefully things are all right and he'll bounce back quickly.
"It's tough. You have a guy who's coming into a new team, and he wants to establish himself. He had a good game tonight, stepping up for his guys and protecting his guys. You never like to see him go down like that."
Parros' injury could restart the debate about whether fighting has a place in hockey. But Montreal's Josh Gorges doesn't think the discussion has merit.
"I see more players get hurt from hits, collisions, from pucks, than I do from fights," he said.
"I don't think saying because a player got hurt in a fight that now we have to talk about taking fighting away. I bet that if you ask George [Parros], he'll be the first to agree with me on that one, too."
Parros joined Montreal this summer after one season with the Florida Panthers. Tuesday's game was his first with the Canadiens.
The Associated Press contributed to this report.