About £62m was pledged to MSF throughout the world for tsunami relief - more than three times the £17m it needed for the first phase of its operations in Asia. Some of the organisation's branches, including those in the UK, are now approaching people who gave money to see if they would be happy for their cash to be channelled into other projects.
If donors want their cash to go to the tsunami, MSF will give the funds back.
Most of the donors contacted so far, either by phone or email, have been in Germany and the US, where some 20 per cent are understood to have asked for their money back.
Marine Buissonniere, international secretary for MSF, said: "We consider it an ethical responsibility to tell donors where we spend funds and to ask them if they would help us in other crises."
At the time of the decision in January to suspend appeals for tsunami donations, the group's director general, Pierre Salignon, said it was important to maintain a transparent relationship with donors.
A spokesman for the charity said that MSF runs programmes in more than 70 countries and still needs funds to support projects in areas largely ignored by the media, such as in the Democratic Republic of Congo and Somalia, and programmes focused on treating infectious diseases such as HIV/Aids, malaria and tuberculosis.
The International Red Cross is also winding down its tsunami appeal, saying that it wants to focus more money on other disasters.