In an essay published on its website quoting "careful estimates", the church said the wives included a 14-year-old and others who were already married.
The Mormon church banned polygamy in 1890 and now excommunicates anyone who practises it.
The church has previously sought to portray Smith as loyal to his first wife Emma.
However, this is not the first time that the church has admitted his polygamy, as previously reported here.
The essay, entitled Plural Marriage in Kirtland and Nauvoo, said: "Joseph married many additional wives and authorised other Latter-day Saints to practise plural marriage."
It said "plural marriage was difficult for all involved"; for Emma it was an "excruciating ordeal".
Multiple marriage and the Mormons
Most of the women were aged between 20 and 40 when Smith married them, the essay added.
The youngest was Helen Mar Kimball, a daughter of two close friends, who he married "several months before her 15th birthday".
It is likely Joseph Smith - who is considered a prophet - did not have sexual relations with all of his wives, as some were "sealed" to him only for the next life, according to the essay.
The Utah-based Mormon religion, officially known as the Church of Jesus Christ of Latter-day Saints, boasts more than 15 million members worldwide.
Polygamy was widely practised by men in the church from the mid-to-late 19th Century, but the revelations about Joseph Smith have shocked followers.
Emily Jensen, a blogger and editor in Farmington, Utah, told the New York Times that members had been saying on social media: "This is not the church I grew up with, this is not the Joseph Smith I love."
What do Mormons believe?
While the practice of polygamy was dropped in 1890, the concept remains in the afterlife. A man can be married or "sealed" to more than one woman after death, but not the other way around.
Church leaders reportedly said the essay was part of an attempt to be truthful and transparent with followers.
It is among a series of essays posted on the Mormon church's website in the past year.
They address topics such as the ban on black men from the priesthood, which was lifted in 1978, and accounts of how Smith translated the Book of Mormon, the church's sacred scripture.
The Mormon church has said for the first time that its founder Joseph Smith had up to 40 wives.