Dewani, 32, who is accused of arranging the contract killing of his wife Anni in Cape Town in November 2010, is under medical treatment after being sectioned and deemed a suicide risk.
His barrister, Clare Montgomery QC, today said the process had been hanging over the businessman like "the sword of Damocles" and he needed "a period of calm".
She told Westminster Magistrates' Court in London that keeping Dewani under medical treatment in Britain for 12 months would increase the speed of his recovery and warned that sending him to South Africa would jeopardise it.
Dewani's psychiatrist says he is making a slow recovery but one damaging factor is his "constant awareness" of the extradition proceedings, the court heard.
Miss Montgomery said Dewani was taking anti-depressants on the advice of his psychiatrist, who believed his depression and PTSD were of moderate severity and had discernibly decreased.
However he still poses a real risk of suicide and is unable to "give an account of himself", possibly because he cannot remember, the court heard.
Dewani could be fit to begin dealing with the extradition process in a year's time, his NHS-appointed psychiatrist believes.
Chief Magistrate Howard Riddle adjourned the hearing to September 18 so a psychiatrist employed by the South African government can examine Dewani and give the court more information about his condition.
Mrs Dewani, 28, who was from Sweden, was shot after the taxi she and her new husband were travelling in was hijacked in the Gugulethu township on the outskirts of Cape Town on November 13 2010.
Taxi driver Zola Tongo and Dewani were ejected by the hijackers before Mrs Dewani was driven away and killed.
She was found dead in the back of the abandoned vehicle with a bullet wound to her neck.
Tongo, who has admitted his part in the crime, claimed in a plea agreement with prosecutors that Dewani ordered the carjacking and paid for a hit on his wife.
The High Court temporarily halted Dewani's extradition in March because of his poor mental health.
Sir John Thomas, the president of the Queen's Bench Division, and Mr Justice Ouseley, ruled it was "unjust and oppressive" to send him to South Africa straight away.
But they rejected claims that he should not be extradited on human rights grounds and said it was in the interests of justice that he be extradited "as soon as he is fit".
Dewani, a care home owner from Bristol, has previously pledged to clear his name.