Special judge Ajay Kumar Kuhar passed the order after Chidambaram was produced before the court through video conference due to lawyers' strike.
The ED counsel contended that the set of evidence in the money-laundering case and the CBI corruption case is different and the PMLA case is more heinous.
The former Union minister has been critical of the Modi government's handling of the economy and has said this is the reason that he is being targeted.
Delhi High Court directed the Tihar jail to provide Chidambaram with home food, mineral water, mosquito protection net and repellant.
Chidambaram has sought interim relief for six days to enable him to consult and get examined by his doctor at the Asian Institute of Gastroenterology (AIG), Hyderabad.
INX Media money laundering case: Delhi court sends P Chidambaram to judicial custody till November 13
The court directed Tihar authorities to provide Chidambaram with medicines, western toilet, security and separate cell.
The plea for interim relief has been moved by Chidambaram in his main bail application in the INX Media money-laundering case.
Sources said Chidambaram was taken to the RML Hospital in the morning and was later shifted to the All India Institute of Medical Sciences.
Chidambaram has asked his family to tweet on his behalf, as he is currently in the custody of the Enforcement Directorate in the INX Media case.
The court said that the other conditions of his custody will be the same, including on providing him home-cooked food.
Justice Suresh Kait issued a notice to the ED on the bail application and asked the agency to file its reply within a week.
Chidambaram, who was on Tuesday granted bail from Supreme Court in the INX media corruption case, continues to be in ED custody since October 17.
The suit alleged that the company was facing continuous “targeted and malafide actions” in the wake of an engineered payment default crisis at one of its subsidiaries, the National Spot Exchange Ltd.
In its 27-page judgement granting bail to Chidambaram, the apex court said he is neither a "flight risk" nor is there a possibility of "his abscondence from the trial".
A bench headed by Justice R Banumathi set aside the Delhi High Court's September 30 verdict denying him bail in the corruption case.