The British charity is accused of concealing the findings of an inquiry into claims staff used prostitutes while delivering aid in Haiti in 2011.
Penny Lawrence said she was “ashamed” and takes full responsibility.
The Charity Commission has launched a statutory inquiry into Oxfam – which denies a cover-up – but details of its scope have not yet been released.
The watchdog says it has concerns the charity may not have “fully and frankly” disclosed everything it knew about the claims despite previous assurances from Oxfam.
Michelle Russell, director of investigations at the commission, said if details had been known it would have dealt with the situation “very differently”.
It comes after an earlier meeting with the International Development Secretary in an effort to protect Oxfam’s funding from being cut.
Ms Lawrence joined Oxfam GB in 2006 as international programmes director, leading teams across 60 countries, according to the charity’s website.
“Concerns were raised about the behaviour of staff in Chad as well as Haiti that we failed to adequately act upon,” she said in a statement.
“It is now clear that these allegations – involving the use of prostitutes and which related to the behaviour of both the country director and members of his team in Chad – were raised before he moved to Haiti.”