Xolile Mngeni, who is serving a life sentence for her murder in Cape Town, was diagnosed with a malignant brain tumour soon after his arrest in 2011.
The news was confirmed by a BBC South Africa correspondent, who said Mngeni was admitted to hospital on Tuesday.
Bristol businessman Shrien Dewani was extradited in April to stand trial, accused of ordering his wife's killing.
Mrs Dewani's body was found with a single gunshot wound to the neck after she and her husband were kidnapped while travelling in a taxi through the outskirts of Cape Town.
He was released unharmed and denies any involvement in his wife's murder.
Three men, including Mngeni, have already been convicted in connection with Mrs Dewani's death.
Mngeni, whose trial was repeatedly delayed while he had surgery to remove a brain tumour, is serving a life sentence for firing the shot that killed Mrs Dewani.
BBC correspondent Milton Nkosi said despite the "belief that he was recovering" Mngeni had been admitted to hospital on Tuesday.
"The Department of Correctional Services told us because of the patient, doctor confidentiality they cannot disclose the details of his condition," he said.
"But what we know is that he is in a serious, critical condition in hospital in Cape Town."
A South African man convicted of murdering Anni Dewani on her honeymoon in 2010 is critically ill in hospital.