"I made this difficult decision based on an open investigation into the nature of some of my personal email correspondence over the past couple of years and for continuing to maintain a professional relationship with a former staff officer," Moran said in a statement on Sunday.
According to US media, the officer is believed to be Chris Servello, a former Navy spokesman who had worked for Moran, reports Xinhua news agency.
Servello allegedly had inappropriate physical contact with a female civilian at a 2016 Christmas party and made sexual advances in a "predatory" manner toward subordinate officers.
"To be clear, my decision to maintain this relationship was in no way an endorsement or tacit approval of this kind of conduct," Moran said in the statement.
The retirement request has been approved by Richard Spencer, Secretary of the Navy.
"This decision on his part to maintain that relationship has caused me to call his judgment into question. Therefore, today I accepted Adm. Moran's request to retire," Spencer said in a statement.
Spencer said John Richardson would remain as the Navy chief a new candidate is nominated and approved.
Moran was nominated in April to succeed Richardson. As the vice chief of naval operations since May 31, 2016, Moran has worked to increase fleet readiness and personnel reform.
Prior to that, Moran, a former naval aviator, served as the vice chief of naval operations until last month, when he was replaced by Admiral Robert Burke.
( With inputs from IANS )