Iraqi officials have described the incident as shameful.
A statement released by the government said Mr Zaidi's actions, which also included him shouting insults at President Bush, "harmed the reputation of Iraqi journalists and Iraqi journalism in general".
Correspondents say the protesters are supporters of Shia cleric Moqtada Sadr - a leading critic of the US presence in Iraq. Smaller protests were reported in Basra and Najaf.
Cannot play media.You do not have the correct version of the flash player. Download the correct version
President Bush ducks as the shoes are thrown
The Iraqi government has demanded an on-air apology from his employer.
An Iraqi official was quoted by the Associated Press as saying that the journalist was being interrogated to determine whether anybody paid him to throw his shoes at President Bush.
He was also being tested for alcohol and drugs, and his shoes were being held as evidence, said the official, speaking on condition of anonymity.
The Cairo-based al-Baghdadiya TV channel said Mr Zaidi should be freed because he had been exercising freedom of expression - something which the Americans had promised to Iraqis on the ousting of former Iraqi leader Saddam Hussein.
"Any measures against Muntadar will be considered the acts of a dictatorial regime," the firm said in a statement.
The programming director for al-Baghdadiya, Muzhir al-Khafaji, described the journalist as a "proud Arab and an open-minded man".
He said he was afraid for Mr Zaidi's safety, adding that the reporter had been arrested by US officials twice before.
"We fear that our correspondents in Iraq will be arrested. We have 200 correspondents there," he added.
Mr Zaidi leapt from his chair at Sunday's news conference and hurled first one shoe and then the other at Mr Bush, who was joined at the podium by Iraqi Prime Minister Nouri Maliki
He [George Bush] deserves to be hit with 100, not just one or two shoes. Who wants him to come here?
A Baghdad resident
The shoes missed as Mr Bush ducked, and Mr Zaidi was immediately wrestled to the ground by security guards and frogmarched from the room.
"This is a farewell kiss, you dog," he yelled in Arabic as he threw his shoes. "This is from the widows, the orphans and those who were killed in Iraq."
Arabic TV stations have been repeatedly showing footage of the incident, which was also front-page news in many papers.
Correspondents say the journalist's tirade was echoed by Arabs across the Middle East who are fed up with US policy in the region.
"He [George Bush] deserves to be hit with 100, not just one or two shoes. Who wants him to come here?" said a man in Baghdad.
But his view was not expressed by everyone.
"I think this incident is unnecessary, to be honest. That was a press conference, not a war. If someone wants to express his opinion he should do so in the proper manner, not this way," said another Baghdad resident.
Also on Monday, Human Rights Watch accused Iraq's main criminal court of failing to meet basic international standards of justice.
The New York-based group said torture and abuse of prisoners before trial appeared common, and legal representation was often ineffectual.
Human Rights Watch said some of the court's failings showed disturbing similarities to those that existed during the Saddam Hussein era.
The group called on Iraq to take immediate steps to protect detainees from torture, and ensure they had access to proper defence and received a prompt hearing.