"We prepared our forces, we raided the house, and we arrested the criminal Ahmed Abed Oweiyed."
Jawad said Oweiyed was the deputy commander of al-Qaeda's military wing in Iraq.
"Through intelligence efforts, we tracked down the criminal who masterminded the killing," he said.
A teenage assailant shot dead al-Obaidi and his bodyguard in Shawaf mosque in the predominantly Sunni neighbourhood of Yarmuk after al-Obaidi had led worship on the weekly Muslim day of prayer.
The assailant then killed three others and wounded 12 by throwing a grenade into a crowd, before killing himself.
Obaidi, born in 1966, was deputy chairman of parliament's human rights committee and head of the biggest Sunni bloc in parliament, the National Concord Front.