The missionaries were serving in Novorossiyk, Russia, which is about 930 miles south of Moscow.
It was unclear why the missionaries were being detained.
“While we are grateful these young men are reportedly in good condition and are being treated well, we are troubled by the circumstances surrounding their detention,” church spokesman Eric Hawkins said, as Salt Lake City's Fox 13 reported.
They reportedly were detained Friday at a local meetinghouse.
Russia enacted anti-terrorism laws in July 2016 that included a provision banning missionary work, the Deseret News noted.
The church complied with Russian law and redesignated the missionaries as volunteers, warning them to comply with local laws and customs.
According to the Salt Lake Tribune, which cited a 2017 report by the U.S. Commission on International Religious Freedom, the Russian law forbids "preaching, praying, disseminating religious materials, and even answering questions about religion outside of officially designated sites."
Missionaries from other religious groups such as Jehovah's Witnesses, Baptists, Buddhists, Muslims, Mennonites, Seventh-day Adventists and Scientologists all have been affected by the law.