Capt. Steven Booker said the paint spill "appears intentional based off of the splatter." Police are reviewing security camera footage to try to identify possible suspects, he said.
The memorial will be closed until the National Park Service maintenance crew can clean up the paint, which is expected to happen later Friday, police said.
National Park Service spokeswoman Carol Johnson said the memorial will be returned to the condition it was in before the vandalism.
"It is not permanent damage," she said. "It can be cleaned."
The memorial, one of the most popular sites on the National Mall, was dedicated in 1922 to the nation's 16th president. It's generally open around the clock to visitors.
Copyright 2013 The Associated Press.