The donation is reported to have been made to the prince in October 2013, more than two years after bin Laden was killed by US security services.
The payment must have been made by the al-Qaeda founder's half-brothers, according to the newspaper.
The prince must have personally received the money in connection with a private meeting at Clarence House in London.
The money must have been handed over in a suitcase, the newspaper writes.
That's where the money went
The donation will, according to The Sunday Times as quoted by Omni, go to the royal residences Clarence House and the Prince of Wales Charitable Foundation.
Clarence House said the money was "immediately handed over to one of the Prince's charities who carried out the appropriate measures and assured us that all the correct procedures were followed".
According to the newspaper, none of the prince's meetings with the half-brothers should be reported among the prince's royal assignments.
The prince's advisers are said to have advised him not to accept the money and then return it.