The American worked as a teacher at a private school in the capital Tripoli and was arrested for "inciting our children to renounce Islam and convert to Christianity", the Internal Security Agency said.
The agency did not provide his name but Libyan media identified him as Jeff Wilson, the founder and head of the consulting firm Libya Business.
In the same statement, the agency said a Libyan national was also arrested for "renouncing Islam" and posted a video of his purported "confession" on its Facebook page.
In the video, a man is seen describing how he was convinced by a foreigner to convert.
Separately the Libyan interior ministry announced Tuesday night that another Libyan had been arrested for "apostasy and the promotion of atheism."
"He was referred to the prosecutor's office after confessing to the charges attributed to him," the ministry said in a Facebook statement.
Islam is considered the state religion in Libya, and while Christians have the freedom to worship there, the majority are foreigners living in the country.
Libya Nabs Alleged Christian 'Proselytizer'
Representative illustration of a person carrying a wooden cross. Taken March 25, 2016.
TRIPOLI - A US citizen has been arrested in Libya for alleged Christian proselytizing, security services in the North African country said Wednesday.