The priest, a diplomatic officer representing Pope Francis at the Holy See Embassy in Washington, has not been named. A Vatican statement says it was notified of the US investigation on August 21.
The priest currently is in Vatican City. Like most diplomats in foreign countries, he has diplomatic immunity from prosecution in the United States.
The Vatican declined to waive diplomatic immunity for its diplomat, a State Department official told CNN.
According to the official, the United States formally requested the waiver.
The Vatican, invoking its status as a sovereign state, says it has opened its own investigation and has begun "international collaboration" in gathering evidence relative to the case.
"We hope the Holy See will be forthcoming with more details," Bishop Daniel DiNardo, president of the US Conference of Catholic Bishops, said in a statement. "This is a serious issue."
Vatican spokesman Greg Burke told CNN that he had nothing to add to the statement except to note that in 2013, the Vatican updated its civil laws to include possession of child pornography as a crime.
According to that new law, promulgated by Pope Francis, possession of child pornography carries a maximum sentence of 12 years in prison.
There are two types of tribunals at the Vatican: one for civil cases, meaning crimes committed by Vatican employees or on Vatican territory which carry regular civil penalties such as fines and jail time, and one for canonical cases, or crimes involving priests, which carry canonical punishments such as laicization, or removing the priest from his position.