The commission has frozen the charity's bank accounts as a "temporary and protective measure".
Kenneth Dibble, director of legal and charity services at the commission, said: "We are working with law enforcement agencies to get to the bottom of allegations of possible terrorist abuse of Crescent Relief funds."
Dibble said the investigation would focus on "the receipt and application of funds that have been raised on the charity's behalf".
Abdul Rauf, former director of the Essex-based charity, which raised money to help victims of the earthquake in Kashmir last October, was arrested in Pakistan on 18 August. His son, Tayib, was arrested in Birmingham on 10 August.