The Rev Andrea Ronconi said small pieces of clothing belonging to the Portuguese shepherd children, who were made saints in 2017, were stolen on Wednesday.
Police are looking for two suspects.
Father Ronconi, priest at the Jesus Christ Divine Worker parish, said he was "heartbroken and mortified" by the theft, which also included copies of a crown and rosary of the Fatima Virgin Mary statue.
Francisco and Jacinta Marto, who reported visions of the Virgin Mary more than 100 years ago, were declared saints on May 13 2017.
The Portuguese town of Fatima has become one of the world's most important Catholic shrines.
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