Lawyers for Stephen Heasley and Andrew Borg - aged in their 30s - claim the pamphlets "were clearly sent to intimidate, threaten and harass the plaintiffs because they are gay men."
The men spent $80 on 100 leaflets (pictured below) to welcome guests to their wedding in Pennsylvania last September but realised the day before the ceremony they had been 80 flyers for the Catholic campaign group Battle Ready.
Titled "Understanding Temptation", they read: "Fight the good fight of the faith.
"The supreme tempter is Satan, who uses our weaknesses to lead us into sin."
A lawsuit filed at the US District Court in Massachusetts on Tuesday urges a judge to declare Vistaprint's actions as "unlawful" and grant compensation for the "economic damages, mental anguish and emotional distress" caused.
Vistaprint, a Dutch company which operates a US hub in Lexington, Massachusetts, said it was investigating, after being made aware of the lawsuit earlier this week.
It claims the delivery was "incorrectly" made by a 3rd party.
The firm said: "To know that any customer could feel treated in such a way, especially during a time that should be filled with joy, is extremely disheartening," the company said.
"We have never been more disappointed to let a customer down.
"Vistaprint in no way condones - and does not tolerate - discrimination against any of our customers based on their race, religion, gender or sexual orientation."
Heasley and Borg or being supported by the New York-based firm, Wigdor Law.
Stay up to date with the latest news stories from a Christian perspective. Sign up to our daily newsletter and receive more stories like this straight to your inbox every morning.