The appeal was filed by the NHL Players' Association on Marchand's behalf, the union said in a tweet Friday.
"I know [the appeal] is this afternoon, I don't know how long it typically takes," Bruins coach Bruce Cassidy said Wednesday. "... Hopefully it goes in his favor."
The incident occurred with 25 seconds remaining in the third period of the Bruins' 4-2 loss to the Pittsburgh Penguins at TD Garden on Feb. 8. Marchand received a minor penalty for roughing and a match penalty for attempt to injure Penguins goalie Tristan Jarry.
Marchand has served three games of the suspension.
"It was a situation that arose and I reacted very poorly," Marchand said Feb. 11. "So it really doesn't matter what started it. In that situation I obviously have to be much better at controlling my emotions and not reacting that way.
"Yeah, was it stupid? Of course it was stupid. I'm not denying that. I absolutely should not have done it."
This is the eighth time that Marchand has been suspended during his NHL career, the second time this season. The forward was suspended three games for slew-footing Vancouver Canucks defenseman Oliver Ekman-Larsson on Nov. 29.
The six games is the longest suspension for Marchand, who had been suspended for five games on two occasions (for clipping Vancouver Canucks defenseman Sami Salo on Jan. 9, 2012, and elbowing New Jersey Devils forward Marcus Johansson on Jan. 24, 2018). He also has been fined five times and has forfeited more than $1.4 million in salary from his previous fines and suspensions, including $448,170.72 on this occasion.
"This one, yes, he lost his discipline," Cassiday said Feb. 10. "No doubt. We'll sit down. … We've had our share of sit-downs over the years. I think Brad's been doing a pretty good job for the most part with controlling his emotions."
Marchand leads Boston with 49 points (21 goals, 28 assists) in 39 games. He did not play in a 6-0 loss to the Carolina Hurricanes on Thursday and a 2-0 win against the Ottawa Senators on Saturday. He is eligible to return Feb. 24 at the Seattle Kraken.
"I know the player I am in this league and for this team," Marchand said. "The last thing I want to do is let my team down the way I did in this situation. I lost my cool, there's no question about it. I've been pretty good at doing that the last number of years. … So I've got to continue to work on being better."
NHL.com staff writer Amalie Benjamin contributed to this report