State government as special public prosecutor argued that the accused are not cooperating with the investigation.
Earlier, the court had stayed the arrest of the five till April 4.
The Mumbai High Court on Friday said it cannot grant any relief to the applicants as the FIR is lodged in Gujarat.
Setalvad, her husband Javed Anand and three others have been booked in a cheating case.
Setalvad and others are accused of misusing the funds collected for Gujarat riots victims and using it for personal needs.
The couple had sought quashing of an FIR filed against them in the Gulbarg Society case.
Setalvad and others have been accused of appealing for funds without the consent of several residents of the Gulberg society.
Ajay Choksi, special public prosecutor, said that the court upheld the argument.
She is alleged to have embezzled funds meant for 2002 Gujarat riot victims.
Teesta and her husband have been booked by the Crime Branch of Gujarat Police on the charges of cheating, breach of trust and under the IT Act.
Setalvad also contended that this was the fifth case registered against her in Gujarat because of her support to the riots victims.
BJP says its quid pro quo for clean chit in fabricated case against scientist.
The CIC,in its order,directed the Inspector General of Police,Law & Order,to provide the information to Setalvad within 45 days and free of cost,she said The Indian Express on Friday.
A single-judge bench of Justice A J Desai,while passing the order,called the special courts order illegal.
Protest will begin from Citizen’s Nagar,Bombay Hotel area tomorrow,on the eleventh anniversary of the riots.