The scene was apparently an amateur glamour shoot.
The nude model was identified in local media as a Canadian tourist, with her accomplices thought to be UK nationals. The three tourists were reported to the Public Prosecutor's Office in Salerno for public indecency.
If found guilty the trio could face fines of up to 30,000 Euros ($50,000).
The Daily Mail identified the model at the centre of the "instagram stunt" as Canadian-national and "would-be-influencer" Savannah Cross. 28-year old Cross was reportedly assisted by a friend from West Yorkshire, Jemma Hopson. They were both in Italy celebrating a friend's birthday.
The photographer was not named but thought also to be an English national.
Local news site Amalfi Notizie, reported the tourists as saying the photo-shoot was for personal mementos from the trip and not a social media stunt.
Positano is one of the many towns along the famously scenic and busy Amalfi Coast. The SS 163 road is normally full of roadtripping tourists and visitors to the nudist beaches, but they rarely wander into town naked.
Last month, two women were caught going for a midnight dip in the Sant'Andrea fountain in Amalfi. Another of Positano's famous landmarks, the baroque 18th fountain is topped by a statue of St Andrew.
American expatriate Laura Thayer told CNN that this summer had been exceptionally busy, with the tourist season stretching out into Autumn. With the barmy weather came equally silly behaviour from tourists.
"Episodes like these are good reminders to be respectful for the places we visit and the people who live there," she said.