John Benizri, who lives on Forsythe Street in Dollard-des-Ormeaux, is the lead plaintiff in the suit.
His lawyer Barbara Villegas says the box was installed near his home last May without proper consultation.
"When they came to install the community mailbox, they didn't ask if it was OK to put it in his property," Villegas told CBC. "It was imposed."
The lawsuit claims Beniziri has suffered "increased noise, traffic, aesthetic displeasures, safety issues and loss of privacy" as a result of the new mailbox.
The lawsuit says his family "is often disrupted at unreasonable hours" by idling cars and loud music. It also says junk mail is sometimes left behind on the lawn.
Canada Post declined to comment, saying the case is before the courts.
This isn't the only Montreal legal battle underway against the postal service.
The city itself is also involved in a federal court challenge.
It will be piggybacking on a current case launched by groups representing seniors, people with disabilities and postal employees.
Last month, Montreal Mayor Denis Coderre took a jackhammer to the concrete slab foundation of a community mailbox in l'Anse-à-l'Orme nature park to protest what he called a lack of consultation on the issue.