The memorial is a statue of a World War II soldier holding a rifle. Most of the paint was on the statue's helmet, the Anchorage Daily News reported.
Police Lt. Paul Honeman said if the perpetrators are caught the exact charge they would face -- either malicious destruction of property or felony criminal mischief -- would depend on how much it costs to clean the statue.
The statue was defaced overnight Tuesday. Passersby who spotted the paint Wednesday morning reported it to police.
By late afternoon, most of the paint was gone, and veterans and their supporters had placed flowers and wreaths at the foot of the statue. An honor guard stood by in the evening.
"Shame on them," said former state Sen. Jerry Ward, chairman of the Alaska Native Vietnam Veterans. "I'm proud to be an American and I'm ashamed of these cowardly people that have done this."