Ahmad Abd al-Ghafur al-Samarrai, head of the government's Sunni Endowments, said the alleged arrest campaign was under way in the Madain area, about 20km southeast of Baghdad.
He said the campaign was to keep them from meeting the 1 September deadline to vote in the planned 15 October referendum on the new constitution, which Sunni Arab negotiators oppose.
Efforts to contact the ministry for comment were unsuccessful because no one could be found to comment.
"Those elements and militia are loyal to sides from outside the country and they are trying hinder the Sunnis' march towards taking part in the referendum," al-Samarrai said.
He demanded the ministry release the Sunnis immediately.
The allegations were made one day after US Ambassador Zalmay Khalilzad appealed to the country's Shia and Kurdish leadership to reach out to the Sunnis so that they might accept the draft constitution, which was submitted to parliament on Monday night.
But the Sunni Arabs negotiating the charter have strongly objected to several proposals, including federalism, references to Saddam Hussein's Baath party and power relationships between provinces and the central government.
Parliament deferred a vote for at least three days to give Shia and Kurdish negotiators time to win over the Sunnis.
Many Sunni Arabs boycotted the 30 January election, enabling Shia and Kurds to win an overwhelming majority in the 275-member National Assembly.
"[Shia elements]are trying hinder the Sunnis' march toward taking part in the referendum"
Ahmad Abd al-Ghafur al-Samarrai, head of Sunni Endowments
But now Sunni clerics are urging their followers to register and take part in the October referendum to reject a constitution, if the final version is unfavourable to their interests.
Al-Samarrai said that if the constitution appears to follow "our Islamic principles, then we will say 'Yes'".
"The Iraqi people are of a high degree of awareness and perception and they are the ones who can say either 'no' or 'yes'".