Shrien Dewani, 31, was suffering post-traumatic stress disorder and was “simply unfit to stand trial”, his lawyer Claire Montgomery told Woolwich Crown Court in southeast London.
She added that it would be “positively inhuman” to keep him in the court.
South African authorities want Dewani, from Bristol, southwest England, to be sent back to the country so he can be put on trial for the murder of his Swedish-born wife Anni, 28, in Cape Town last November.
District Judge Howard Riddle said he allowed Dewani to leave court with “some considerable hesitation”.
The 10-minute hearing, attended by the dead woman’s parents, was adjourned until Tuesday.
Dewani’s extradition proceedings began in May but were adjourned while a psychiatric report was compiled. He has been granted bail but is staying in a
secure mental hospital in Bristol for his own safety.
The newlyweds were being driven through the dangerous township of Gugulethu
when their taxi was hijacked on November 13. Dewani was thrown out of the vehicle while his wife was driven off and shot dead.
He apparently told a witness that he “needed a way out” of his marriage to Anni.
Taxi driver Zola Tongo was sentenced to 18 years in prison after admitting his part in the crime, but claimed Dewani ordered the car-jacking and paid for a hit on his wife.
Dewani denies any wrongdoing.