The public should only give to tsunami appeals run by registered charities, the UK watchdog has warned.
One e-mail scam has asked for money by international transfer
The Charity Commission says it cannot guarantee that organisations without a charity number will donate the funds they collect to victims of the tragedy.
It also says misleading leaflets asking for donations were distributed in East Anglia, London and Lincolnshire.
The warning comes after Essex police arrested two men over an allegedly bogus tsunami appeal in Colchester.
The men have been bailed pending further inquiries.
Charity Commission chief Andrew Hind said it was "incomprehensible" that anyone would want to take from those who have "absolutely nothing".
He said: "I would urge the generous public to make their cash donations to an established appeals fund such as the Disasters Emergency Committee."
The commission also said that donations of clothes should be made to a registered charity shop instead of unregistered door-to-door collectors.
But Global Concern, which describes itself as a "charitable organisation" but is not a registered charity, disagrees with the commission.
Global Concern is not registered with the Charity Commission
It has been handing out leaflets in East Anglia and Lincolnshire asking for donations of clothes for tsunami victims.
The organisation's coordinator, Bill Johnson, says he will channel all aid through the Disasters Emergency Committee (DEC).
"We are just trying to help the situation. We will do everything we say on the leaflet and any money we raise will go straight to the DEC," he said.
Mr Johnson says his organisation only operates in East Anglia and Lincolnshire, but believes leaflets are being distributed without his permission in other areas of the country.
And the Metropolitan Police are probing claims that several bogus charity websites have been set up following the tsunami.
There is widespread concern that fraudsters will try to benefit from the Asian disaster.
One e-mail scam has already been uncovered.
An organisation calling itself the Solid Foundation Humanitary Fund Asia has sent e-mails asking for donations by international money transfer.
It originates from Nigeria - where the notorious "419" e-mails came from.
The 419 scam promised huge wealth in return for a small investment and succeeded in conning over £100m from recipients worldwide in just one year.
The Charity Commission says the public needs to use common sense before donating to any organisation.
But both police and the commission stress that the most important thing is for the public to continue helping tsunami victims.