A Vatican statement said that an arrest warrant had been issued for Carlo Alberto Capella, which was carried out by the Vatican Gendarmerie.
"The accused is being detained in a cell in the barracks of the Gendarmerie Corps, available to the judicial authorities," the statement said.
The arrest warrant was issued by the investigating magistrate of the Vatican City State Tribunal.
Capella, who was in office until last year, was recalled from Washington last September by the Vatican.
It is the latest case the Catholic Church has faced after repeated criticism for the way it has handled scandals over paedophile priests.
The US State Department notified the Vatican in August through diplomatic channels of a possible violation of child pornography laws by a member of the diplomatic corps of the Holy See in Washington, the Vatican said in September. The United States made "an official request" for the man's diplomatic immunity to be lifted but the Vatican refused, said a US official on condition of anonymity.
In February, the Vatican said it had renewed its anti-paedophile panel in a bid by Pope Francis to quell the global scandal over the sexual abuse of children by priests. The panel had come under fire from two high-profile members, former sex abuse victims who quit at what they saw as a lack of reform and obstruction at the highest level of the Catholic Church.
Victims have come forward from across the world over the past two decades accusing priests of sex crimes, unleashing one of the biggest crises faced by the Catholic Church.