The commission says that thieves have obtained charities' bank account details from Gift Aid forms and used the information to set up standing orders to steal funds from charities.
It advises that the best way for charities to protect themselves against the scam is to change those bank accounts whose details are published for Gift Aid purposes into deposit-only accounts.
Sign, the National Society for Mental Health and Deafness, uncovered the scam when it spotted two new standing orders adding up to hundreds of pounds set up on the charity's account.
Fortunately, the charity noticed them quickly, contacted its bank and stopped the standing orders before any money was lost. Police are now investigating.
Steve Powell, chief executive at Sign, said: "It is a sad fact of modern times that charities are having to constantly fight against clever con artists. We all have a duty to be aware of the forms these scams can take and to take steps to protect charitable funds."
The commission praised Sign for being vigilant about checking its bank details and acting so swiftly that it did not lose any donations.
Charities are being advised by the commission to check bank statements thoroughly for rogue payments. Andrew Hind, chief executive at the commission, said: "This is a particularly worrying scam because it requires no contact with the charity and leaves charities with no opportunity to become suspicious."
Andrew Watt, head of policy and deputy chief executive at the Institute of Fundraising, supports the commission's advice to charities but admits to being worried about the reaction of donors.
He said: "As with any charitable scam, the real danger here is that it will result in an increased wariness among donors and potential supporters about how their money is being spent.
"However, the only thing donors really can do is to make sure they know that their donations are going to the organisations they intend to support."
He added: "It's a great example of charities' vigilance that Sign spotted the discrepancies so quickly. We would encourage other charities and the banking sector to be equally on the ball in observing the appropriate security measures."