The Bishop of Husi, Barladeanu, 51, decided to step down "for the peace and good of the church", the patriarchy said.
He maintains his innocence and has not made any public comment.
The statement was issued at the end of a two-day Holy Synod where a sex scandal was discussed for the first time in its 92-year history.
There has been uproar in Romania over Bishop Barladeanu and another scandal involving a priest who had sex with a male student as believers are demanding more accountability from the church.
Outrage was heightened as the two cases involved homosexual acts. The church, however, insisted the bishop would have been similarly chastised if the alleged sexual misdemeanours had involved a woman.
Barladeanu will no longer hold an official position, but he will remain a monk.
The statement said the resignation was the best outcome, because an investigation would last months and would "prolong the situation of uncertainty of the bishopry of Husi" in north-east Romania.
However, church critic and political analyst Stelian Tanase said the church, which counts more than 85% of Romanians among its flock, should have issued a stronger statement.
He said: "I think that the Synod should have come out with a strong decision to condemn such shameful practices for servants of the church... Instead, they preferred a cover-up. "
The church also blamed "an aggressive campaign of some media outlets aimed against the Romanian Orthodox Church, often with the complicity of some errant priests".
It added that "all believers ... should respect the discipline of the church and permanently renew their spiritual lives".
