Laila Ibrahim Issa Jamool is being kept shackled to her baby in Omdurman women's prison after she was convicted by a court in the capital Khartoum July 10.
President Omar Hassan al-Bashir said Sudan would adopt a "100 per cent" Islamic constitution after the breaking away of non-Muslim South Sudan a year ago.
Jamool's husband accused her of adultery, illegal under the country's penal code. Her death sentence is the second to be passed in Sudan for the offence in the last few months.
Women's rights group Strategic Initiative for Women in the Horn of Africa has assigned lawyers who have appealed against the conviction.
Amnesty International said the conviction did not meet international legal standards and also violated Sudanese criminal law.
The group said the stoning sentence was imposed "after an unfair trial in which she was convicted solely on the basis of her confession and did not have access to a lawyer".