City and state politicians announced they will not attend or march after OutVets was told they would be excluded this year.
The decision came after a 9-4 vote by parade organisers on Tuesday night.
An OutVets representative said the ban was due to the rainbow flag on the group's logo.
"They said people felt that rainbows represent the gay community," Bryan Bishop, the founder of OutVets, told the New York Times.
"I told them if that's the case, then every picture of a rainbow in the parade that leads to a pot of gold needs to be removed," Mr Bishop added.
Several sponsors announced that they are withdrawing support for the event, and Budweiser-brewer Anheuser-Busch said it was "evaluating" its participation.
Politicians across Massachusetts, the first state to legalise same-sex marriage, in 2004, reacted with outrage to the news.
Boston Mayor Marty Walsh released a short statement saying: "I will not tolerate discrimination in our city in any form."
He said he would skip the event, and added "anyone who values what our city stands for should do the same".
Michael Flaherty, a Boston city councillor, called the decision "disgusting" and added that "whoever voted for this is a nitwit".
Massachusetts Governor Charlie Baker and US Senator Edward Markey have also said they will boycott the parade unless the organisers reverse their decision.
A member of the parade committee, which is organised by the South Boston Allied War Veterans Council, said the group would hold an emergency meeting on Friday.
According to the groups' code of conduct, LGBT groups are not banned, but the event does "not allow the advertisement or display of one's sexual orientation as a topic that should in any way be depicted as a theme of our parade".
OutVets was first permitted to march two years ago, becoming the first LGBT group to march in the Boston parade.
The Boston St Patrick's day parade is facing a boycott after organisers decided to bar a gay veterans' group from participating this year.