The lawsuit comes days after the US Supreme Court's landmark ruling that effectively struck down bans on same-sex marriage in Louisiana and several other states.
Louisiana began issuing marriage licenses to same-sex couples yesterday. The state had been the last to do so.
The American Civil Liberties Union Foundation of Louisiana, the Forum for Equality Foundation and six New Orleans residents lodged their challenge of the governor's May 19 order in state court in Baton Rouge.
He swore to uphold the laws of Louisiana. This lawsuit seeks to hold him to that oath," Marjorie Esman, executive director of the ACLU of Louisiana, said in a written statement.
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Indian-American Jindal's "Marriage and Conscience" executive order prohibits state agencies under his control from denying licenses, benefits, contracts or tax deductions in response to actions taken because of someone's "religious belief that marriage is or should be recognized as the union of one man and one woman."
The lawsuit claims Jindal tried to bypass the Legislature and make new law on his own, exceeding his constitutional authority and violating the separation of powers between the executive and legislative branches.
Jindal's top lawyer referenced the order in a legal memo as licences began being issued, saying officials who object to same-sex marriage on religious grounds don't have to officiate at such weddings or approve the licences.
Jindal's office didn't immediately respond today to a request for comment about the lawsuit. When he issued the executive order, the governor framed it as a protection for Christians who oppose same-sex marriage, in anticipation of the Supreme Court decision.
Businesses opposed the bill, much like they did for similar proposals in Indiana, Arkansas and other states. Tourism leaders said it could heavily damage one of Louisiana's most important industries.
Critics in the legislature called Johnson's bill an unnecessary distraction from important work of balancing next year's budget and stabilizing the state's finances.