It is understood she had been rebuked by the Presbyterian Church in Ireland (PCI) for taking part in an LGBT church service shown by RTÉ in 2023 and was under an investigation for attending the 2024 Dublin Pride parade.
She is retired from Christ Church, Sandymount in Dublin.
It is understood she was previously censured for having an elder, Stephen Smyrl, who was openly living in a same sex relationship.
In a statement released this week, Rev Meyer confirmed that she had resigned during a meeting of the Presbytery of Dublin and Munster on 3 December.
"The particular claim which has been the common theme of these acts of discipline, as best as I can determine, is that by my teaching and actions I have disrupted the peace and unity of the Church," she said. "And further, that following censure, I failed to seek to preserve that peace and unity.
"Precisely how I did this was never clearly stated but assumed. The specific trigger for all the complaints, however, in spite of their different circumstances, seems to have been a link to my pastoral support for members of the LGBTQ+ community and my appearance in public in their company, although this was never specifically stated."
Professor Ruth Whelan, an historian at Maynooth University, attended two hearings with Rev Meyer as "a witness and scribe".
She said the first hearing was about her attending an LGBT church service televised by RTE and the second because she walked in the 2024 Pride Parade in Dublin.
Prof Whelan noted that in 2018 PCI elders and ministers voted to exclude anyone in a same sex relationship from full membership; not to baptise their children and to break communion with the Church of Scotland.
"As a result, in my view, the PCI has turned in on itself; it no longer recognises the legitimate rights of conscience of church members who dissent from clearly controversial decisions," she said.
Rev Meyer's former elder at Sandymount, Stephen Smyrl, also defended her.
“Rev Katherine Meyer walked alongside me and my husband, Roy Stanley, at this year’s Dublin Gay Pride," he said. "She did so not as the complainants have suggested, in order to damage the peace and unity of the Presbyterian Church in Ireland, but rather to show solidarity with a marginalised group, to acknowledge gay people’s dignity and humanity."
A PCI spokesperson said: “The resignation of anyone from office within the Church is a matter of regret, but ultimately a personal decision for each individual. "However, we recognise that this resignation was offered within the context of judicial processes within the church.
“While Dr Meyer has the right to her own view on those processes, nonetheless, on several separate occasions representative groups within the Presbyterian Church in Ireland have found her to be at fault. This included both Dr Meyer’s local Presbytery and on more than one occasion the duly appointed senior body at General Assembly level, a group which consists of ministers and elders, men and women from across all 19 of our Church’s Presbyteries in Ireland."