The Washington Post reported it wasn't clear whether she had anything to do with similar green paint vandalism found earlier Monday on the base of a statue in front of the Smithsonian Castle and Friday on the Lincoln Memorial.
District of Columbia police had not released the woman's name, the newspaper said.
Paint was first discovered poured on an organ in the cathedral's Bethlehem Chapel about 2 p.m. and later in children's chapel, the Post said. The cathedral was closed to the public Monday afternoon, the newspaper said.
A Smithsonian spokeswoman said green symbols were found painted on the granite base of a bronze statue of Joseph Henry, the museum's first secretary, during the morning hours.
District of Columbia police were working with the U.S. Park Police in investigating the incidents.
Cathedral spokesman Richard Weinberg said the paint on the organ was still wet and it appeared it could be removed.
A National Park Service spokesman said about 90 percent of the paint had been removed from the Lincoln Memorial.