From the BBC:
25 June 2012
Last updated at 16:55 GMT
In a letter to new Greek Prime Minister Antonis Samaras, Mr Rapanos said he was stepping down due to ill health.
Mr Rapanos has been in hospital since last week receiving treatment for stomach pains.
Mr Samaras is himself recovering from eye surgery which has caused him to miss this week’s EU summit.
Mr Rapanos, who is chairman of the National Bank of Greece, was named finance minister last week as part of Greece’s new three-party coalition government.
However, he was rushed to hospital last Friday before he could be sworn in and has been in hospital ever since.
The BBC’s Mark Lowen in Athens say there has been speculation that Mr Rapanos is unhappy with the makeup of the new cabinet, and other reasons may lie behind his decision to resign.
Several names have been touted as Mr Rapanos’s replacement, including the former Prime Minister Lucas Papademos, he says.
The new coalition will be keen to fill the post swiftly, our correspondent adds.
Mr Samaras, meanwhile, underwent routine surgery on Saturday for a damaged retina and the operation was said to have been a success.
As well as missing the EU summit, Mr Samaras’s health problems also led the “troika” of rescue lenders to postpone a visit to Athens.
Inspectors from the EU, European Central Bank and IMF had been due to review Greece‘s progress in meeting bailout conditions on Monday.
Debt-stricken Greece is under huge international pressure to fulfil the terms of its international bailout.
The banker put in place by the new Greek government to oversee the country’s surrender to plunder by its creditors resigned for health reasons late on Monday: here.