The order also prevents publication of his alleged victim's name or any details that could identify her.
The man was arrested by New Zealand police last August on suspicion of killing his former partner in Switzerland 15 years ago. No charges have been laid but he could face manslaughter or murder charges if he is extradited.
The arrest came after an international search involving Interpol, New Zealand police and Swiss authorities.
Swiss police allege the man fled the country after killing the woman in her apartment.
At the Auckland District Court this morning Judge Paul said while all evidence Swiss police had linking the man to the murder was circumstantial - it could be inferred by that evidence at a trial that he was involved.
He said there was a "very strong case" against the man and a the probability of conviction was "certainly a likelihood".
The man has been on bail since his arrest last year but Judge Paul today remanded him in custody. He said that as circumstances had changed and the man was now facing serious charges for the most serious of crimes it was too risky to continue bail.
"I'm simple not prepared to allows this man to remain in the community with these factors now clearly at play," he said.
The final decision on whether the man is extradited now lies with the Immigration Minister. The man has 15 days to appeal Judge Paul's decision.
Mr Illingworth said a decision had not been made on whether an appeal would proceed.
