Bishop Kieran Conry quit the role last month saying he had been "unfaithful to his promises as a priest".
Since then he has faced allegations of an affair with a married woman.
An inquiry has been ordered and will investigate whether any of the accusations against Bishop Kieran involve 'potentially vulnerable female adults'.
It is not known who will lead the inquiry, which will last around six months. The findings will never be published.
The Archbishop of Southwark, the Most Rev Peter Smith, is currently overseeing the diocese.
A spokesman for him said the inquiry would check whether there were any 'safeguarding' implications related to Bishop Kieran's conduct.
When he resigned, the bishop told churchgoers his actions "were not illegal and did not involve minors".
He also apologised to Catholics in his diocese, saying he was "sorry for the shame" he had brought.