Auditors found overpriced supplies, salaries for non-existent aid workers and fake customs bills.
The disease, which raged between 2014 and 2016, claimed at least 10,000 lives.
It required a massive humanitarian operation costing hundreds of millions of dollars to bring it under control.
As Ebola spread across Liberia, Sierra Leone and Guinea, the Red Cross Federation in Geneva was dispersing cash donations to the national Red Cross societies in each of those countries – altogether a sum of about $100m.
An investigation by Red Cross auditors has revealed that in Liberia $2.7m disappeared in fraudulently overpriced supplies or in salaries for non-existent aid workers.
In Sierra Leone, Red Cross staff apparently colluded with local bank workers to skim off close to $2m while in Guinea, where investigations are ongoing, around $1m disappeared in fake customs bills.
The Red Cross told the BBC’s Imogen Foulkes in Geneva that it is deeply sorry for the losses.
The organisation adds that it has introduced stricter financial rules, and promised to hold any Red Cross staff involved to account.
Fraud involving donor money is every aid agency’s nightmare, our correspondent says.
The Red Cross is the world’s best-known humanitarian organisation, and this revelation will be damaging, she adds.