The ministry said he was arrested in the desert outside Cairo with a "smuggler attempting to escape to Sudan," south of Egypt.
During his time in office, a court had sentenced Qandil to a year in prison for not carrying out a ruling to re-nationalise a company that had been privatised in 1996.
A Cairo appeals court upheld the sentence in September.
An unpopular prime minister, Qandil kept a low profile after Morsi's overthrow by the military in July.
He represented an alliance of pro-Morsi Islamist groups in meetings with European mediators who tried to defuse tensions with the military-installed government.