The reports by Italian newspapers on Tuesday say the relationship started four years ago with shared personal revelations in the confessional before evolving into a sexual affair and then an extortion racket that cost the priest at least 350,000 euros (A$475,000).
At one point, the priest is reported to have handed over his entire monthly stipend to the woman, as well as an inheritance he received years earlier.
The payments reportedly began with the aim of helping the family of the cash-strapped woman but were soon made in order to prevent her from revealing evidence of the affair.
The woman, now 32 and identified in reports only by her first name, Ramona, has been detained by authorities on charges of extortion.
The case was revealed after the now penniless 80-year-old priest filed a complaint detailing threats he received and the financial burden he suffered.