Gilbert Costa was attacked by youths early today while he was guarding the Saint Rita Church at Mathurapur, Pabna district, some 175 kilometres from Dhaka.
"We have detained three suspects after the attack. We suspect the attack was motivated from previous enmity," Chatmohar Police Station Officer-in-Charge Ahsan Habib was quoted as saying by the Daily Star.
Further details will be known after the investigation, he said.
Police suspect the incident was the result of a family feud.
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"They fled the scene as soon as local shopkeepers came to Gilbert's rescue," Rozario added.
Costa has been admitted at the Pabna General Hospital.
Bangladesh has suffered a spate of attacks on religious minorities. In October 2015, a church pastor was attacked in Pabna's Ishwardi upazila.
The attack in Pabna is the latest in a series of attacks and murders carried out in the similar fashion across Bangladesh in the past two years.