Shabazz, 46, also allegedly violated a judge's order to remain in New York State, the New York Daily News reported. She was arrested Tuesday.
A judge in Queens ordered her held without bail pending a hearing Jan. 6, the New York Post said.
Shabazz pleaded guilty in June to opening credit cards in the name of Khaula Bakr, whose husband was one of her father's bodyguards. She was given probation on condition that she repay $55,000 at the rate of $1,229 a month.
At Tuesday's hearing, probation officials said she had repaid none of the money, the News reported. They also said she was living in St. Albans, Vt.
Shabazz had $800 on her when she was arrested, police said.