Francis Pereira was arrested by a team of special investigation officers from Curtorim village in South Goa, a senior police officer said.
"The accused was planning to desecrate an idol in the village. But he tried to flee from the spot on seeing a police team," he said.
The police team nabbed him after a brief chase, he said.
The police officer said, "During initial questioning, he admitted to having carried out the desecration of the religious symbols."
The Cross in at least 12 places and a temple have been vandalised in south Goa district since July 1.
The latest of such incidents was reported from Margao town yesterday.
Chief Minister Manohar Parrikar ruled out handing over the investigation to CBI, claiming that he had full faith in the state police.