State police arrested Wayne Bent, 66, on three counts of criminal sexual contact of a minor and three counts of contributing to the delinquency of a minor, said Department of Public Safety spokesman Peter Olson.
Bent was being held on $500,000 bond at the Union County Detention Center in Clayton and was scheduled to be arraigned on Thursday.
According to the affidavit for the arrest warrant, Bent is alleged to have touched three girls in 2006 and 2007. All of them were under 18 at the time, and one of them was 12.
Bent, who goes by the name of Michael Travesser and claims to be the Messiah, is the leader of The Lord Our Righteousness Church, whose members moved in 2000 to a remote, former ranch near the Colorado line that they call Strong City.
The state Children, Youth and Families Department recently had removed two girls and one boy from the site, and said it was interviewing a third girl who had left the compound earlier.
Those three girls are the same girls cited in the affidavit, according to Olson.
Wayne Bent's son, Jeff Bent, who also lives at Strong City, said the charges against his father were "false charges."
"He hasn't done anything wrong. He hasn't committed any crimes," the younger Bent said in an interview with AP Online Video.
"I don't question that there are things that have happened here that are shocking to people's cultural norms, but ... the things that have occurred here are not illegal," he said.
He also said he did not know to what extent Wayne Bent would take part in the legal proceedings, saying, "he will do what God instructs him to do."
Wayne Bent has acknowledged having sex with followers - including his daughter-in-law - and lying naked with virgins. He said the virgins asked for sex, but he refused.
In a posting on the church's Web site, he denied that there was any molestation of children or adults at the community. A former member of the sect has estimated there are about 50 people on the compound. The three children removed last month are believed to have been the only minors there.
Bent accused the state of kidnapping the children.
A posting attributed to Bent on the church's Web site Monday said:
"Jesus had not committed any crimes, so the authorities had to invent some crimes to crucify him over. It is the same for me also. I have committed no crimes, but many crimes are being imagined and concocted in the minds of men to try and kill me again."
Bent had predicted the end of the world last Oct. 31.
Church leader arrested on sex charges in northeast N.M.