ROME—The Vatican arrested one of its own diplomats Saturday on suspicion of violating laws against child pornography, setting the stage for the first trial for that crime in Vatican City.

The Vatican said in a statement that its police force, known as the gendarmerie, had arrested Italian Msgr. Carlo Alberto Capella under a Vatican law setting penalties for anyone who “distributes, disseminates, transmits, imports, exports, offers or sells child pornography.”

The...