According to Amnesty, the 64-year-old accountant was working for an Evangelical Christian organisation prior to her arrest on the morning of 12 February when four men, who identified themselves as members of the NSS, entered the house and arrested her without providing a reason.
Later the same day, the men returned and confiscated her passport, as well as the house's electronic equipment, including laptops, a desktop computer, tablets and a router.
"Following Salwa Fahmi Suleiman Gireis' arrest, plainclothed men visited the family farm and put cupboards containing bibles under seal. They reportedly killed the pigs that were being raised there and stole a motorcycle," AI said in its statement, adding that the NSS has also summoned a relative of Gireis for questioning.
AI said it feared Gireis may be "detained in conditions amounting to ill-treatment".
While her family has been allowed to visit her once and bring medicine for her high blood pressure, she has not been charged and has been denied access to a lawyer.
"Amnesty International considers Salwa Fahmi a prisoner of conscience, held solely for her peaceful work with a religious organisation," the human rights organisation said.
It urged Sudanese authorities to release Gireis immediately and unconditionally and to cease ongoing harassment and intimidation of her family members.
More on Sudanese persecution of Christians.