The coffers are only around half full for its 1.2-million-Swiss-franc (768,000-euro, 932,000-dollar) programme in Belarus, Russia and Ukraine, said Anna Nelson, spokeswoman for the International Federation of Red Cross and Red Crescent Societies.
The sum is needed to fund aid operations this year and next, she told reporters.
So far, only one country has come up with money to meet the costs: Ireland, with a donation of 500,000 euros (785,000 Swiss francs, 610,000 dollars) which is being paid over three years.
The Chernobyl nuclear plant erupted on April 26, 1986 and the Red Cross launched its aid effort four years later.
"The programme addresses the basic health needs of those living in contaminated areas," said Nelson.
Since 1990, the Red Cross has assisted more than three million people, screening 800,000 of them for thyroid cancer, said Nelson.
One of the main planks of the programme is the use of mobile laboratories to provide cancer screening and care in remote areas.
Thanks to the Red Cross, early diagnosis has ensured high survival rates: only two of the 1,120 cases of thyroid cancer detected since 1997 have been fatal.
The programme remains vital because the number of cases is growing, said Nelson.
The Red Cross aid effort also includes handouts of vitamins to 50,000 children in the region.
"Despite the recognition that support for affected areas remains essential and despite clear indicators showing a continued increase in cases of thyroid cancer, donor interest has steadily declined. And that's something we're very worried about," said Nelson.