The complaint said displaying the Ten Commandments violates the First Amendment of the U.S. Constitution, and "simply cannot be reconciled with the fundamental religious-freedom principles that animated the founding of our nation."
Nine families, including several clergy, with children in public schools filed the lawsuit in the Baton Rouge, Louisiana federal court, seeking an injunction against the law.
Louisiana became the only U.S. state requiring displays of the Ten Commandments when Governor Jeff Landry, a Republican, signed the law on June 19.
The law is also part of a broader push by conservative groups to make expressions of faith a more prominent part in society.
Some hope that such laws, when challenged in court, could eventually receive a friendly welcome at the U.S. Supreme Court, which has a 6-3 conservative majority.
That court in 1980 declared unconstitutional a Kentucky law requiring the display of the Ten Commandments in public schools.
But in 2022, the court sided with a high school football coach in Washington state who said he had a constitutional right to pray with his players at the 50-yard line after games.
Landry's office did not immediately respond to requests for comment.
In signing the Louisiana law, Landry said displaying the Ten Commandments would help expand faith in public schools.
Reuters sources say prosecutors are recommending the move, after finding the plane maker violated a settlement related to two fatal crashes.
"If you want to respect the rule of law, you've got to start from the original law-giver, which was Moses," he said.
The plaintiffs said the law violates the First Amendment's prohibition against state establishment of religion.
They also said the law violates the First Amendment's free exercise clause by pressuring parents and children to accept the state's favored religious message.
"It is our children's right" to decide what views to accept, plaintiff Darcy Roake, a minister in the Unitarian Universalist Church whose husband is Jewish and also a plaintiff, said on a conference call with reporters.
In the Christian and Jewish faiths, God revealed the Ten Commandments to Hebrew prophet Moses.
Louisiana's law requires an easy-to-read, poster-sized display of the Ten Commandments in all classrooms, from kindergarten through public colleges.
It also requires a statement that the Ten Commandments had been "a prominent part of American public education for almost three centuries."
Such a statement could suggest that the Ten Commandments have historical, as well as religious, value.
The lawsuit was assigned to U.S. District Judge John deGravelles, who was appointed to the bench by Democratic President Barack Obama.