Shafiq's candidacy could see him stand against Sisi, who has yet to officially declare his candidacy but looks all but certain to run in and dominate the election next year.
A Reuters witness at the airport said Egyptian authorities escorted Shafik in a motorcade that was waiting for him outside the airport.
With airport security high, Shafik landed in a private plane in Cairo airport on Saturday evening, the airport sources said.
The family and lawyer said they planned to file complaints with the prosecutor's office around Shafiq's whereabouts. "We presented him with every facility and generous hospitality despite our severe reservations about some of his positions", Gargash said.
"We were about to leave to travel to France".
Shafiq's family and lawyer said Sunday they had lost contact with him after what they called his deportation from the United Arab Emirates to Cairo, days after announcing his intention to run for president of Egypt next year.
According to information by sources at Cairo's International Airport, when Shafiq's plane landed almost 50 family members and his loyalists met him at the airport.
She explained that these "officials" informed him that he must leave the UAE without his daughters while they told his daughters that they are welcome to stay in the UAE.
A Gulf source familiar with the matter had told Reuters: "Shafik has publicly asked to go to Egypt and his wish will be met".
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Shafiq's lawyer, Dina Adly announced his arrest on her official Facebook page.
One Egyptian judicial source said on Saturday Shafiq did not face any criminal cases in Egypt.
"(Shafik) took refuge in the UAE and ran away from Egypt after the results of the 2012 presidential election.
Shafik is not the only person planning to challenge Sisi in the presidential election.
May Shafik said on Friday he was preparing to depart, first for Europe and the United States before returning to Egypt to start his campaign.
"The authorities in UAE have arrested Shafiq at his house in order to deport him to Egypt", Adly said. The UAE denied placing movement restrictions on Shafik.
The UAE's Foreign Minister Anwar Gargash later responded in a series of tweets, saying there was "no obstacle" to Shafik's departure from the UAE.
Mr Morsi himself was ousted by the military in July 2013 following mass anti-government protests, with Mr Sisi elected president a year later. Sisi's supporters see him as key to stability following the upheaval that followed the 2011 Egyptian revolt that toppled president Hosni Mubarak.
But his government is struggling to crush the insurgency in the North Sinai region and has also enacted painful austerity reforms over the past year to revive the economy which critics say have eroded his popularity.