Juventus striker Ronaldo allegedly travelled to Courmayeur, 150 kilometres north-west of the Serie A club’s Turin headquarters, for his girlfriend Georgina Rodriguez’ birthday.
When contacted by AFP, Juve declined to comment.
Rodriguez, who turned 27 on Wednesday, apparently posted a video of the couple on a snowmobile on Instagram.
She later removed it, but it was picked up by several Italian news sites.
Under current Italian coronavirus rules, the couple should not have left the town of Turin. They each risk a fine of 400 euros ($485).
The 35-year-old footballer has been embroiled in coronavirus-related controversy before.
Ronaldo then tested positive himself and returned to Italy to spend a couple of weeks in isolation at home.
At the time, Italian Sports Minister Vincenzo Spadafora accused the star of “violating” coronavirus restrictions.