The 5-1 decision by the state's highest court said Stanley M. Shepp has a constitutional right to express his beliefs about plural marriages and multiple wives even though bigamy is illegal.
Shepp considers himself a fundamentalist Mormon, though the Mormon church officially renounces polygamy.
"Where, as in the instant matter, there is no finding that discussing such matters constitutes a grave threat of harm to the child, there is insufficient basis for the court to infringe on a parent's constitutionally protected right to speak to a child about religion as he or she sees fit," Justice Sandra Schultz Newman wrote.
The girl's mother, Tracey L. Roberts, testified that Shepp's interest in polygamy broke up their marriage, and expressed concern that he may introduce the girl to men in preparation for marriage at age 13, according to the court opinion.
Roberts and Shepp have joint legal custody of the girl, who is now 13.
A county judge had prohibited Shepp from teaching the child about his polygamist beliefs — at least until she turned 18 — and that decision was upheld by the state Superior Court.
Newman wrote that the state's interest in enforcing the anti-bigamy law "is not an interest of the 'highest order"' that would trump a parent's right to tell a child about deeply held religious beliefs.
Neither Roberts nor Shepp appeared to have listed phone numbers, and their respective attorneys did not immediately return phone messages seeking comment Thursday.
The Church of Jesus Christ of Latter-Day Saints renounced polygamy in 1890 as part of a deal to grant statehood to Utah. The church now excommunicates those who practice or advocate it. But some people who describe themselves as fundamentalist Mormons continue to believe in polygamy, and an estimated 30,000 in the West practice it.