Iraqi security officers and U.S. secret service agents leapt at the man and dragged him struggling and screaming out of the room where Bush was giving a news conference with Iraqi Prime Minister Nuri al-Maliki.
The shoes missed their target about 15 feet (4.5 metres) away. One sailed over Bush's head as he stood next to Maliki and smacked into the wall behind him. Bush smiled uncomfortably and Maliki looked strained.
"It doesn't bother me," Bush said, urging everyone to calm down as a ruckus broke out in the conference room.
When asked about the incident shortly after, Bush made light of it. "I didn't feel the least threatened by it," he said.
Other Iraqi journalists apologised on behalf of their colleague, a television journalist.
Bush arrived in Baghdad earlier on Sunday on a farewell visit before he leaves office in January. The U.S.-led invasion in 2003 to topple Saddam Hussein triggered years of sectarian bloodshed and insurgency in Iraq, killing tens of thousands.
(Reporting by Matt Spetalnick; Writing by Michael Christie; Editing by Elizabeth Piper)