Shafik, a former air force commander and government minister, has been seen as the strongest potential opponent of President Abdel Fattah al-Sisi, who is widely expected to run for a second term next year.
His family said Shafik was picked up at the family home in the United Arab Emirates (UAE) on Saturday and taken by private plane back to Cairo. A Reuters witness said Egyptian authorities escorted him in a convoy from the airport.
UAE authorities confirmed he left the Emirates, but Egyptian officials have not commented on the case.
"We know nothing about him since he left home yesterday," Shafik's daughter May told Reuters. "His lawyer hasn't been able to reach him. If we was deported he should have been able to go home by now."
The family and lawyer said they planned to file complaints with the prosecutor's office about Shafik's whereabouts.
Egypt's foreign ministry said it was not responsible for the case. The interior ministry could not immediately be reached for comment.
One Egyptian judicial source said Shafik, who narrowly lost a 2012 presidential election, did not face any criminal cases in Egypt. He was acquitted, or had charges dropped, in several cases in the past, including for corruption.
Sisi has yet to announce his own intentions for the presidential election, saying only he would follow the will of the people.
Critics say under Sisi's presidency thousands of dissidents have been jailed, the government has shut down independent media and heavily restricted the conducting of polls in what rights groups call an unprecedented crackdown.
His supporters dismiss criticism over rights abuses and say any measures are needed for security in the face of an Islamist terrorist insurgency that has killed hundreds of police and soldiers in the last four years.
Shafik had said on Wednesday he would run for president in a surprise announcement from the UAE, where he has been based. Several other lower-profile candidates have said they will run as well.
As military commander, Sisi led the ousting of former president Mohamed Mursi of the Muslim Brotherhood in 2013, before winning his own landslide election a year later. Sisi's supporters see him as key to stability after the upheaval following the 2011 revolt that toppled president Hosni Mubarak.
But his government is battling a stubborn Islamist terrorist group fighting in the North Sinai region and has also enacted painful austerity reforms over the last year to revive the economy but that critics say have eroded his popularity.
(Reporting by Amina Ismail; Writing by Patrick Markey; Editing by Mark Potter)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)