This decision follows calls by governors' leaders this week for the unnamed priest's resignation.
Jane Phillips, chair of the National Association of Governors and Managers, said resignation should not necessarily imply he was a continued danger, but it would be in the best interests of the school.
Neil Davies, chair of the National Governors' Council, said: "The honourable thing to do, especially with this man being a Christian, would be to resign as a governor.
"Governing bodies are encouraged to be transparent in their dealings, and this resignation would be for the sake of transparency."
The priest's parish duties include being governor of a Roman Catholic school in London, but he has no contact with children.
The Archdiocese of Westminster initially supported his right to continue in this post. But they have now decided to review this.
"All relevant guidelines have been observed, but in the light of concerns being raised, we are looking at the commitment again," said an adviser to the Archbishop of Westminster.
BBC Radio 4's Today programme reported this week that the priest, then in his 30s, "inappropriately interfered" with a teenager at a seminary in 1986.
His victim confronted him via email this April, and within hours the priest wrote back admitting what he had done and asking for forgiveness, the programme reported.
The priest contacted church authorities, who brought in their own child protection team. They referred the matter to police, but the victim chose not to proceed further.
The priest was suspended while a risk assessment was carried out. He was allowed to return to his post and remain a school governor after the recommendations of the assessment were implemented.
Oona Stannard, director of the Catholic Education Service, said: "I would expect nothing but the highest standards from any governor. The welfare of the children is paramount. I have no reason to think this has been compromised."