Sunday visitors to the Cathedral of John the Divine noticed the headless statue, prompting church officials to contact police, Officer Kathleen Price said.
A dollar bill with Washington's image cut out was left atop the neck of the stone statue, which stands near the front of the church, Price said.
The statue is about 3-feet (a meter) tall. It is part of a church collection of historical figures spanning 20 centuries, said Herb Katz, a cathedral spokesman.
Washington represents the 18th century, a statue of William Shakespeare stands for the 17th century and an Abraham Lincoln figure symbolizes the 19th century.
In December 2001, an electrical fire severely damaged two rare 17th century tapestries at the cathedral, which is the principal church of the Episcopal Diocese of New York, reports AP.
The building, a neo-Gothic landmark, is in the Morningside Heights neighborhood on the edge of Harlem, a few blocks from Columbia University. The Encyclopedia of New York City describes it as America's largest cathedral. It is big enough to hold two football fields.