Special Judge Arvind Kumar order came on Vadra's plea seeking to travel abroad for a medical check-up as a tumour in his large intestine had been detected.
The Enforcement Directorate had strongly objected his plea mainly for London, apprehending that Vadra might tamper with the evidence if he was allowed to go there.
The case against Vadra relates to alleged ownership of overseas assets worth 1.9 million pounds. The charges against him pertain to undisclosed foreign assets and entities to evade tax.
Vadra was granted anticipatory bail on April 1 on the condition that he would not leave the country without permission and join the probe whenever required.
Vadra has submitted a medical certificate from Sir Ganga Ram Hospital here.
He had told the court that his doctor had advised him to get a second opinion and therefore he wanted to go to London.
Representing the ED, Solicitor General Tushar Mehta told the court that the doctor had not essentially asked Vadra to take a second opinion in London but only mentioned he can take it "if he wishes so".
He said the investigation in the case was at a crucial stage and there were chances Vadra may not return.
The ED argued that there were treatment facilities available in India.
Countering the ED's submission, Vadra's counsel said Vadra will not go to those places where the agency has objections.
The defence counsel said Vadra's medical condition can worsen with the passing of time.
( With inputs from IANS )