"I can think of no better use of our time and our resources than to make the images and ideas ... available to billions of people worldwide,'' Schmidt said.
Google has taken some 14,000 photographs of the museum and its artefacts, and the images will be available online in early 2010, he said.
Artefacts from other sites across the country will also be photographed as they become available and then put on the internet.
Artefacts looted
The national museum in Baghdad, which only reopened in February after nearly six years, was among many institutions that were looted or set ablaze following the ousting of Saddam Hussein, the former Iraqi president, in 2003.
Amira Edan, the museum's director, said around 5,000 of the estimated 15,000 artefacts that were looted have been recovered so far.
Edan said Google's project marks another step toward normalcy for the museum, and will provide a useful tool for scholars studying ancient Mesopotamia.
US troops were heavily criticised for not protecting the treasures at the museum and other cultural institutions at the time of the looting.
Schmidt said: "Most American companies are not yet operating in Iraq.
"We would like to show that it's possible to do business in Iraq, that Iraq is an important market that will grow quickly, that it's sufficiently stable that you can begin your business operations here and that it's a safe place to be."
The museum holds artefacts from the Stone Age through the Babylonian, Assyrian and Islamic periods