The appeal relates to a high-court ruling last week upholding the order of the central bank to remove the 70-year-old microfinance pioneer as managing director of the Garmeen Bank, which he had founded and is now 25 percent state-owned.
Yunus is a Nobel Peace Prize laureate.
A Supreme Court bench headed by Chief Justice A.B.M. Khairul Haque adjourned the hearing to examine the lower court's ruling, the Bangladesh Daily Star reported.
The appeal said Yunus had been appointed to the Grameen Bank post with the approval of central bank in 1990.
The central bank, in a letter, said Yunus had failed to seek its approval before he was reappointed to his Grameen position. The lower court upheld the central bank's contention that Yunus had crossed the regulation age of 60 to serve as managing director, and also said that a managing director cannot serve indefinitely.
Yunus's microfinance campaign provides small loans to help poor entrepreneurs who would be ignored by major banks, a concept that has been adopted in many countries.