Peter Kiare, 41, was arrested on Tuesday in the Queens borough of New York, where he had been working as a guest preacher at a church.
He could face a one-year prison sentence if convicted.
Father Kiare is the third Roman Catholic priest arrested in a month in the diocese of Brooklyn - which includes the borough of Queens.
The incident comes as the Catholic Church remains embroiled in a sex abuse scandal in several US states.
Allegations
Father Kiare is accused of sexual abuse and endangering the welfare of a child during a Father's Day excursion to a New York beach on 16 June.
He is a member of a religious order of missionary priests based in Ireland called the Holy Ghost Fathers.
Church officials said he was only a guest of the Queens parish and had not been officially assigned to the church where he preached.
They say Father Kiare arrived in New York on 11 June to preach and raise donations at the church.
New York's Roman Catholic archdiocese - one of the largest and most powerful in the United States - has been rocked by sex scandals in recent weeks.
Pressure
On 23 May, a priest from India was arrested in Harlem and charged with molesting a 12-year-old girl at her home in Brooklyn three years earlier.
And last Friday, a visiting priest from Nigeria was arrested in Texas and charged with raping a woman in Brooklyn.
There is growing attention across the United States to allegations of child abuse against priests, after scandals from Boston to Florida.
The Roman Catholic church itself is also facing mounting criticism following allegations that it protected sexual offenders for decades.
New York's cardinal, Edward Egan, has been accused of helping cover up such cases when he was a bishop in Connecticut.