The arrest comes after al-Sudani was accused of graft linked to public food rations, known as the Public Distribution System (PDS).
On Monday, Nuri al-Maliki, the Iraqi prime minister, said that al-Sudani had resigned due to the allegations.
Al-Sudani, a member of al-Maliki's Shia Dawa faction, had been questioned twice by the parliament over the accusations before he resigned.
The Iraqi judiciary issued an arrest warrant for him on Saturday.
Al-Saedi has also accused al-Sudani's two brothers of misappropriating millions of dollars related to imports. One is currently in police custody and the other's whereabouts are unknown.
A recent leaked report by Iraq's anti-corruption committee, which investigated more than 10,000 complaints of government corruption, said billions of dollars were being lost because of corruption, with the worst offenders being the ministries of interior, finance, health, defence and education.