Father Reinaldo Lures was a military chaplain and it is alleged that a group opposed to the government could be responsible for his death.
There is currently huge political unrest in Venezuela as protestors call for the president's resignation.
The Bishop of La Guaira, His Exc Mgr Raúl Biord Castillo, confirmed the news in a statement.
"We are waiting for investigations by state agencies that may clarify the reason and the circumstances of his death," he said.
He added: "As Christians, we deplore this death that is added to many other deaths due to the violence and insecurity that we live in the country."
Meanwhile, Pope Francis has called for peace in the country.
He said: "Do not be afraid of peace. Cohabitation, dialogue, reconciliation and union are not a defeat but a victory, because who wins is the human being created by God in order to be able to live in harmony."
More than 40 people have died in violent protests in Venezuela since February.