He was detained as part of an investigation into a corruption scandal dating back to his time as Guatemala's Finance Minister, BBC reported.
According to the report, his arrest is not related to his role at Oxfam but it will mount further pressure on the charity, which was reeling from revelations that its staff hired prostitutes in Haiti.
"He has assured us that he has co-operated fully with the investigation in the confidence he did not knowingly transgress rules or procedures," Byanyima was quoted as saying.
"I am ashamed that this happened on my watch and I take full responsibility," she added.
Lawrence issued her statement as Oxfam executives were responding to a demand for full information from the British government's Department for International Development (DFID) which has threatened to cancel its multi-million dollar funding package.
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