Father Renato Salvatore, general superior of the Camilliani order dedicated to caring for the sick and poor since the 16th century, was arrested along with five other people accused of helping carry out the Machiavellian scheme, police said in a statement.
The group arranged a fake interrogation for the two members of the congregation on the basis of a fictitious legal inquiry.
"The 'kidnapped' clerics were therefore prevented from taking part in the election" on the day in May that Salvatore was voted in, police said.
Businessman Paolo Oliviero, implicated in a series of other police investigations, was the brains behind the plot and by way of thanks was given a bigger role in running the order's hospital, the statement said.
The order's head curate, Paolo Guarise, expressed the Camilliani's "great surprise and sorrow" after Salvatore's arrest, saying in a statement that he hoped the police probe "will shed light on the affair".
The Camilliani, also known as the "Order of the Ministers of the Sick", have worked in several countries since 1586 but are on the decline, with just 1,200 priests left, seconded by 20,000 lay members.