Al-Zeidi has been in custody since the Dec. 14 outburst at Bush's joint news conference with Prime Minister Nouri al-Maliki. Thousands demonstrated for al-Zeidi's release and hailed his gesture.
But concern was raised about his welfare after allegations that he had been severely beaten and tortured in detention.
The case's investigating judge has said the journalist was struck about the face and eyes, apparently by security agents who wrestled him to the floor after he hurled his shoes, forcing Bush to duck for cover.
Maitham al-Zeidi was not available to comment on the visit, but another brother, Dhargham, told The Associated Press that he was told the wounds had healed.
"Muntadhar was in a good shape ... and his morale was high. Yesterday was his birthday and some patriotic officers there organized a party for him and brought birthday cake," Dhargham al-Zeidi said.
The case became a focus for Iraqis and others in the Muslim world who resent the U.S. invasion and occupation. But it also embarrassed al-Maliki, who was standing next to Bush at the time. Neither leader was injured.
Al-Zeidi had been due to face a trial in December on a charge of assaulting a foreign leader, which his defense team said carried a maximum sentence of 15 years. But an appellate court is considering a motion to reduce the charges to simply insulting Bush.
Defense lawyer Dhia al-Saadi said it was a matter of freedom of expression.
"Al-Zeidi's act was symbolic and in no way was it a murder attempt," he said, adding that he had been allowed to meet his client only once.
"I submitted many petitions to the judge of the case and I expect to meet Muntadhar next week," he said.
Al-Zeidi's act of defiance transformed the obscure reporter from an employee of a minor TV station into a national hero to many Iraqis fed up with the nearly six-year U.S. presence here.
But his brother said information about the international wave of support had been kept from the journalist.
"Some officers told him that half of the Iraqis were against him. But he was very happy when he heard that all the Iraqis support him. He even cried when he heard that there were demonstrations on his behalf even in the United States," Dhargham al-Zeidi said.
The brother who met with Muntadhar al-Zeidi was taken by bus to the detention center, and two army officers supervised the meeting.
The journalist is currently being held alone in a comfortable room with a bed and a TV set, his brother said. "He is being visited frequently by doctors. The food is very good," the brother added.
Al-Zeidi stood by his attack on Bush. He stressed that he meant no offense to the Iraqi prime minister but didn't want to miss his chance to send Bush a message, the brother said.
"He said he could not wait until al-Maliki left the room to throw his shoes because then Bush would also leave and that historic opportunity would be lost," he said.
Muntadhar al-Zeidi actually feared he would be killed by guards after throwing his shoes and read his last prayers before going to the news conference, his brother said.
"So for him it does not matter for how long he would be imprisoned," his brother said, "because the important thing is that he restored the honor of the Iraqi people."
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Associated Press writer Sameer N. Yacoub contributed to this report.
