All social media will now be handled directly through the club, according to the report.
Bellamy's blast comes after star winger Josh Addo-Carr posted photos on social media of a hunting trip with South Sydney fullback Latrell Mitchell, which saw both players fined $50,000 for breaching social distancing laws.
It is forbidden in New South Wales to gather in groups of more than two people you don't live with. Cleary and the women in the photos were not staying 1.5m away from each other, as required, either.
Under NSW guidelines, people can leave their house only for work, essential shopping, exercise, medical appointments and compassionate visits.
Cleary was later seen dancing with a group of women in a now-deleted pair of TikTok videos on the same weekend he was photographed for breaking social distancing rules.
The newly emerged videos could contradict his claim that the women only visited his home for 10 minutes.
The NRL confirmed to Fox Sports Australia that the integrity unit is reviewing the videos.