The disappearance of Fr Jose Luis Sanchez Ruiz had sparked two days of unrest in the town of Catemaco.
He is the third Roman Catholic priest abducted in the eastern Mexican state since September. The other two were found shot dead by a roadside.
Clerics said Fr Sanchez Ruiz had been targeted because he fought corruption.
"He had received threats in recent days because he is a defender of human rights," said Fr Aaron Reyes, a spokesman for the diocese.  "He has criticised the system of corruption and the crime problem in Catemaco."
Bishop Fidencio Lopez said Fr Sanchez Ruiz "had been dumped, with notable signs of torture'' at an undisclosed location.
About 30 priests have been killed in Mexico in the last decade, most of them in areas heavily affected by drug violence.
In addition to the two priests killed in Veracruz in September, another was found dead after disappearing in the state of Michoacan.
Mexico's Catholic Media Centre says the country is the most dangerous in the world to be a priest.
At least 15 priests have been murdered in the country since President Enrique Pena Nieto took office in 2012.
Veracruz and Michoacan have been plagued by years of violence from drug cartels and other organised crime.
A priest abducted in the Mexican state of Veracruz has been found alive after three days, but with signs of torture, Church officials say.