Deputy Chief Justice Abdul Rahman Sharfi added that any doctors who refuse "the rule of Allah" will themselves face prosecution, the Sudan Tribune reported.
He made the comments at a news conference in response to strong criticism from human rights groups concerning last month's amputation of the right hand and left foot of a man found guilty of armed robbery.
"We cherish the book of Allah (Koran) and not the Hippocratic Oath," said Sharfi.
He said if doctors refuse to follow Islamic law the government is prepared to train and qualify some judges to perform court-ordered amputations.
Sharfi said more than 16 amputation sentences have been carried out since 2001.
Sudanese President Omer Hassan al-Bashir has said he wants to adopt a "100 percent" Islamic constitution now that the South has split off.