The trustee, who was treasurer of the scout group, told Third Sector he was "a BNP member and proud of it".
A spokesman for the Scout Association said the charity had had a written policy on membership of particular political parties since the mid-1990s.
He said: "Members of parties based on racist beliefs who do not accept our principles of racial equality and international understanding are barred from membership of the Scout Association."
A list of 13,500 names and addresses of BNP members was posted online last week. On the BNP's website, leader Nick Griffin confirmed that the list was genuine.
The scouts forbids membership of four political parties: the National Front, the BNP, the Nation of Islam and Hezbollah Tehiyah.
The spokesman said the trustee had been informed of his suspension in writing this week. "He will have to make a choice: if he wants to be a member of the BNP, he cannot be a member of the scout movement." Trustees of four other charities are on the list.
A spokeswoman for the Charity Commission said charity trustees could be members of any political party provided they did not use their charity as a vehicle for their political views.
"A charity can have a policy that trustees are not members of a particular political party if it is deemed to pose a potential risk to the charity, for example in terms of reputational risk," she said.
She added that a charity did not need to have a written policy in order to make decisions about what was in its best interests, and that trustees must be given the chance to respond.
When the list was leaked, BNP leader Nick Griffin said: "The publicity about the high quality of our membership has massively improved our image."
The party's policies include "an immediate halt to all further immigration, the immediate deportation of criminal and illegal immigrants and the introduction of a system of voluntary resettlement for immigrants who are legally here".