The imprisoned nephew of blind Chinese activist Chen Guangcheng is suffering from appendicitis and has been denied medical parole, his father says.
Bottles and rocks had also been thrown at their family home, he added.
Chen Kegui was sentenced to more than three years in jail for assaulting local officials who were looking for his uncle, who had fled house arrest.
Chen Guangcheng took refuge at the US embassy in Beijing and was eventually allowed to travel to the US.
The activist - whose flight from house arrest caused a diplomatic crisis between Washington and Beijing - has long expressed fears his relatives would face reprisals.
"[Chen Kegui] was diagnosed with appendicitis on 24 April," Chen Kegui's father, Chen Guangfu, told the BBC.
"I was told [on Monday] by the prison that the appendicitis had become acute. We were so worried. We filed a medical parole application, but the prison refused to accept the filing," he said.
Cheng Guangfu said a physician at Linyi prison told him they were treating Chen Kegui's appendicitis with heavy doses of antibiotics.
But he said he was told the prison did not have the capacity to perform surgery, and that if Chen Kegui needed surgery he must be transferred to a proper hospital.
Jared Genser, founder of advocacy group Freedom Now, also wrote to the UN rapporteur on torture on Monday appealing for help.
"In light of the life-threatening nature of Chen Kegui's illness, the denial of adequate medical treatment in this case presents an urgent threat to his well-being," he said.
Calls to Linyi Prison and Linyi Prison Hospital by the BBC went unanswered.
Separately, Chen Guangfu told the BBC that his home had been attacked.
"This morning, I spotted a car coming towards the edge of my courtyard. Just as I was puzzled, I heard banging, and they threw beer bottles and rocks into my courtyard," he said.
Calls to the police were not answered, he added.
Cheng Guangfu has previously described other forms of harassment at his home, including dead ducks and chickens being left at his doorstep, rocks being thrown at his windows and threatening notes being stuck on his front door.
Campaigners say that relatives of activists in China are often harassed with the intention of intimidating the activists.
Chen Guangcheng, a self-taught lawyer, campaigned against forced abortions under China's one-child policy and was jailed for four years in 2006 for disrupting traffic and damaging property.
He was placed under house arrest after his release in 2010. After he fled to the US embassy, his relatives' homes were raided and his nephew, Chen Kegui, was detained by police after a scuffle.
The authorities said that Chen Kegui hacked and wounded officials. However, family members said he acted in self-defence after the officials stormed his home and assaulted his parents.