The lawsuit filed Wednesday in Boston says photographs and articles published three days after the bombings made it appear the FBI was pursuing 16-year-old Salaheddin Barhoum and 24-year-old Yassine Zaimi.
The two were featured on the front page under the headline "Bag Men."
The suit accuses the newspaper of libel, negligent infliction of emotional distress and privacy invasion. It alleges the newspaper subjected them to "scorn, hatred, ridicule, or contempt."
The plaintiffs are seeking unspecified monetary damages.
A spokeswoman for the Post referred a question Thursday to the newspaper editor's comments in April, when he said the two weren't identified as suspects and the newspaper stood by its story.