On Friday Masutha declined Xolile Mngeni's application, which was made on June 11, spokesman Mthunzi Mhaga said in a statement.
The medical parole advisory board recommended Mngeni, who was diagnosed with a brain tumour in 2011, be placed on medical parole.
The application was referred to the correctional supervision and parole board, which declined the application. This was on the grounds that there were no appropriate arrangements for Mngeni's supervision, care and treatment in the community into which he would be released.
"The minister considered the application of the offender and directed that the social worker urgently provides a comprehensive report that addresses the aftercare (medical treatment) needs of the offender," Mhaga said.
"We are of the view that the correctional centre where he is incarcerated has the necessary resources to provide him with adequate medical assistance."
Mngeni was reportedly admitted to Groote Schuur Hospital, Cape Town, last month.
The Western Cape High Court jailed Mngeni, and co-accused Zola Tongo and Mziwamadoda Qwabe, for life in 2012 for killing Dewani.
Mngeni was also sentenced to 15 years' jail for robbery with aggravating circumstances and to five years for possession of an unlicensed firearm and ammunition; to run concurrently with his life term.
Dewani, 28, was shot dead in Gugulethu on November 13, 2010, in an apparent staged hijacking. Her body was found the next day.
Her husband Shrien was extradited from Britain to South Africa in April. He is currently undergoing psychiatric observation at Valkenberg Hospital.
Shrien Dewani is charged with conspiracy to commit kidnapping, robbery with aggravating circumstances, murder, kidnapping, and defeating the ends of justice.
He could stand trial by October if a mental health panel finds he is fit.