Meriam Yehya Ibrahim, her American husband, Daniel Wani, and their two children were detained as they were leaving the country for the United States.
Ibrahim's lawyers said that agents from the National Intelligence and Security Services (NISS) detained the family and they were being interrogated at national security headquarters in the Sudanese capital.
"It's very disappointing," her lawyer, Elshareef Mohammed, said.
"They were very angry. They took us [the family's lawyers] outside, and took the family to a NISS detention centre. They have not been given access to lawyers."
BBC quoted Abdullahi Alzareg from the ministry of foreign affairs saying that Ibrahim had been arrested because she did not have the correct travel documents.
He said that she was using emergency South Sudanese papers with a US visa despite being a Sudanese citizen.
She would be freed "soon", the official said.
On Monday the court had let her go after she was condemned in May to hang for apostasy under the Shariah law.
Sudan's SUNA news agency said that the "appeal court ordered the release of Mariam Yehya and the cancellation of the (previous) court ruling".
Lawyer Elshareef said that the appeal court had put no restrictions on her travelling. The lawyer suspected that political differences within the government over the case may have played a part in the decision to prevent her leaving.
"I'm very concerned. When people do not respect the court, they might do anything," said Elshareef.
Ibrahim was born to a Sudanese Muslim father and an Ethiopian Orthodox mother. Her father left when she was six. She was raised by her mother as a Christian.
The case, according to her lawyers, started after Ibrahim's brother filed a complaint against her, alleging that she had gone missing for several years and that her family was shocked to find she had married a Christian man.
The sentencing had triggered a global outrage.
She was locked up with her toddler son and gave birth to a daughter 12 days into her confinement in the women's prison in Omdurman, near Khartoum.
After the birth of their second child, Wani said he did not believe she would be released.