Matiri said a guard was shot dead during the arrest.
The US statement made no mention of any violence and US officials had no immediate comment.
Though the statement did not identify al-Darraji, details of the operation given by the US military coincided with those given by al-Sadr's office.
Senior Shia officials close to the government of Nuri al-Maliki, the Iraqi prime minister, say US and Iraqi forces are mounting a campaign to seize leaders in the movement in an effort to quell sectarian violence that is pushing Iraq towards civil war.
"Bush's strategy has failed totally in Iraq"
Dimos, Hania-Crete, Greece
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In the statement, the US military said: "In an Iraqi-led operation, special Iraqi army forces captured a high-level, illegal armed group leader during operations with coalition advisers."
It said he was suspected of leading "punishment" activities, an apparent reference to informal courts applying justice according to strict interpretations of Islamic law.
These were said to include "kidnapping, torture and murder".
Al-Mahdi Army arrests
Matiri said: "We are angry. This is a kind of revenge. Sheikh Darraji deals with the media. He is not a military man."
He said the US forces were trying to provoke the movement into a violent response but added: "We will not retaliate."
Al-Maliki said this week that some 400 al-Mahdi Army members had been arrested in recent days in southern Iraq.
Al-Sadr himself has publicly distanced himself from violence blamed on his al-Mahdi Army supporters, whom the US has called the biggest threat to the security of Iraq.
Fellow Shia leaders say they are negotiating to keep Sadr and his political movement inside the main Shia bloc while at the same time they hope to disarm his followers.