Until now, the recommendation of just one doctor was sufficient.
Swaminathan has told BBC Sinhala Service that he has instructed the prisons commissioner general to follow the new requirement with immediate effect.
The prisons ministry will study the medical reports to take a decision, he said, adding the measure follows complaints of irregularities in admissions to prison hospital.
Lalith Weeratunga, Anusha Pelpita admitted to prison hospital, media reported
There have been criticisms that politicians, other influential persons including rich underworld figures ordered to be imprisoned get admitted to prison hospital to enjoy privileges.
The latest to be admitted in that manner are former secretary to the president Lalith Weeratunga and ex-TRC director general Anusha Pelpita.
They have been sentenced to three years rigorous imprisonment after being found guilty to a charge of misusing public money to distribute Sil clothing during the 2015 presidential election campaign.