The accused, Lauri Love, 31, who has Asperger's syndrome, is accused of stealing sensitive data from NASA and the US military.
His lawyers say he faces up to 99-years in prison if he is found guilty.
However, his father, Alexander, a vicar who works as a prison chaplain in Suffolk, is worried because his son is suffering depression at the prospect of extradition and he fears he will not survive the ordeal.
Revd Alexander Love has called Britain's extradition treaty with the US unfair and "rendition by judicial process" and asked Britain, "the best court system in the world," to hear the trial instead.
Speaking ahead of his son's appearance in court for an extradition hearing on Tuesday, Alexander Love said: "What worries us most is that my son has stated emphatically that he will kill himself if he gets extradited to America.
"He just couldn't countenance being away from his mum and dad, we are like his carers - we look after him.
"I'll be honest with you, we come home some days and we think he might have killed himself. We live with this and we are scared at times.
"When your first baby is born you go and check they are breathing while they are asleep in the cot, you just want to make sure. We are worried about what might happen to him.
"And he has on more than one occasion sat there scratching away said to us 'mum, dad if it wasn't for you I would kill myself'. If he gets taken to America, he won't have that support."
Lauri Love will appear at London's Westminster Magistrates Court on Tuesday for a hearing about whether he should be extradited to the US.
The vicar is worried that the American prison system will be too harsh for his son to survive.
He said: "They said if someone is deemed suicidal, they put them in isolation to protect them and make them wear a suicide smock. We couldn't believe they were actually proud of this plan.
"The America bill of rights says no American citizen should be subject to cruel and unusual punishment. Well, they want to take a boy who has got Aspergers and very bad eczema and take him away and put an ocean between him and the people who are best suited to look after him - his mother and father."
Revd Love said his son became very depressed as a teenager when the family moved home and he "retreated" into computers.
Over the following years, he has struggled with his mental health and has since been diagnosed with Asperger's.
Listen to Premier's Hannah Tooley speak to Revd Alexander Love here: