Prosecutors detained Olteanu on Friday pending an investigation into charges he accepted 1 million euros in 2008 to influence the government over a key appointment.
He remains under house arrest for the next month. Olteanu has denied wrongdoing, but said he would resign to avoid damage to the central bank's reputation, the first senior bank official to have been investigated and lose his job.
The central bank, which holds a rate-setting meeting on Thursday, has said the investigation would not impede policy making. A replacement for Olteanu on the nine-member bank board must go through parliament, which is currently on summer recess.
A senior Liberal party member said on Monday the bank should have no problem operating with eight board members until September.
The Romanian leu was flat on the day at 4.455 per euro.