A man in Lancashire used the pretext of collecting for earthquake victims to con his way into homes and steal valuables. And some unregistered appeals are operating in London.
The commission said it was aware of the Lancashire incidents and had contacted Muslim community groups and the police to reinforce the message that people should donate only to registered charities.
Jamil Munir of the Pakistan Welfare Association said: "I am absolutely gobsmacked that somebody could do this - it is inhuman. For somebody to take advantage of this tragedy is very disappointing when communities are already suffering stress."
Milly Ahmed, a Muslim from north London, has noticed posters for unregistered charities. "I wouldn't give to these appeals," she said.
A spokesman at the Muslim Council of Great Britain said the Muslim community had a responsibility to tackle the conmen, who could strike again during Ramadan.
"The mosque is one place for donations," he said. "Islamic Relief and Muslim Aid are registered charities we suggest Muslims should give through."
Mahmood Hassan, chairman of Islamic Aid, said many people had applied to the charity to collect money on its behalf but it had yet to authorise anyone. "We don't want to register any Tom, Dick or Harry and then realise that after collecting on our behalf they have disappeared with the money," he said.