Lan Mercado told the BBC the cases took place in the Philippines, Bangladesh and Nepal before she started as regional director two years ago.
She said the scale of misconduct was “not comparable” to that in Haiti, where Oxfam faces claims staff paid vulnerable people for sex.
Oxfam is meeting the Charity Commission as part of an inquiry by the regulator.
The commission has launched a statutory inquiry into Oxfam – which denies covering up the behaviour of its staff in Haiti after the 2010 earthquake – but details of its scope have not yet been released.
It is also looking into claims that Roland van Hauwermeiren – the charity worker at the centre of the sexual misconduct scandal in Haiti – was employed by Oxfam two years after he left another aid agency because of concerns about his behaviour.
Ms Mercado, who oversees 14 countries, said she was aware of similar cases involving Oxfam workers in Asia between 2009 and 2013.
She said they went largely unreported publicly and had been dealt with internally “according to specified policies”, although the situation should not be defined as a “cover up”.
But in an interview with the BBC, she said: “Haiti has taught us we need to do a lot more.”
She said more effort should be made to alert the authorities and other potential employers about allegations.
“That’s a practice that we need to start,” Ms Mercado added.
“You know the funny thing about cases like this is that we always see them as reputational risks.
“But the way to manage reputational risk is not to keep silent.. we need to be thinking about the reputation of the sector as a whole.”
Her comments come after actress Minnie Driver stood down from her role as a celebrity ambassador for Oxfam.
In a statement the Good Will Hunting and Hope Springs star said she was “nothing short of horrified” by the allegations.
Organisations including Marks & Spencer and the Duke of Edinburgh’s (DofE) Award have also said they are considering their association with the charity.
More than 1,200 Oxfam donors cancelled their direct debits on Saturday, Sunday and Monday. On average there are 600 cancellations per month.
However, Oxfam said there had been an increase in one-off donations on Tuesday as well as 44 new regular gifts [direct debits] – the highest since March 2017.
International Development Secretary Penny Mordaunt has said she would “not hesitate” to cut government funding to charities that failed to put robust safeguarding measures in place.
At an event in Stockholm to find ways to end violence against children, she said: “No organisation is too big, or our work with them too complex, for me to hesitate to remove funding from them if we cannot trust them to put the beneficiaries of aid first.” (Courtesy BBC)