Hisham Kandil had been sentenced to one year in prison for failing to implement a court ruling to renationalise a textile firm.
"Security forces managed to arrest Hisham Kandil, former prime minister, in carrying out a court order issued against him. He was caught in a mountain area with smugglers trying to flee to Sudan," Egypt's interior ministry said in a statement.
Kandil was appointed in July 2012 by Morsi after he won Egypt's first democratic elections that followed the fall of President Hosni Mubarak in 2011. Morsi was ousted by the army in July after protests against his rule.
The judgment against Kandil was issued in April 2012, while Morsi was still in office and was upheld by a higher court in September. The case related to the sale during the Mubarak era of a state-owned firm to a private investor.
The arrest came as the death toll in a suicide bomb attack on a security compound in Nile Delta reached 15.
