General Abdel Karim Khalaf, an interior ministry spokesman, said the operation had been approved by Nuri al-Maliki, the prime minister.
He said that al-Maliki had ordered government troops to take possession of all government buildings in Basra within 48 hours.
Journalists in Basra reported that al-Sadr supporters had refused to leave.
Salah al-Obeidi, a Sadr spokesman from Najaf, in central Iraq, called the move "a provocation that will induce people to resort to force".
"The objective of the security forces is to further aggravate tensions and it shows the government's claims that it is not targeting Sadr supporters to be false," he said.
The al-Sadr office in Basra is in an old Olympic committee building.
The incident comes only weeks after clashes between Iraqi forces and the al-Mahdi Army, when al-Maliki launched a crackdown on Shia fighters in the port city.
The clashes quickly spread to other Shia regions of Iraq, killing and wounding hundreds of people.
The US military confirmed that, in a separate incident earlier this week, a unit of Iraqi troops abandoned their positions in Baghdad's Sadr City district, a poor Shia suburb of Baghdad where support for al-Sadr is strong, during a battle with the al-Mahdi Army.
The battle in Sadr City is seen by many as a key test for Iraq's army after the earlier botched Basra crackdown.