Police said they were attempting to trace the operator of the remote aircraft, who was within the grounds of the 67m (220ft) high monument at the time.
Visitors have regularly been arrested and fined for relieving themselves on the 138ft-high monument, or climbing on it naked to pose for pictures.
The inscription declares that the 60-foot-high monument is the tomb of Simon, a devout Jew who the Bible says cradled the infant Jesus and recognized him as the Messiah.
In the two-story high monument, the water is collected from rain, but also from various spring sources as far as 50 miles away from the capital if necessary.
The 12-foot-high monument, representing bookshelves with the pages facing outward, was designed by the British artist Rachel Whiteread.
Unveiled in 1935, the 42 m high monument of granite, travertine, and copper often serves as the focal point of public gatherings and official ceremonies in Riga.
Italy agreed to send the 82-foot-high monument back in 1998, but a border war between Ethiopia and Eritrea put those plans on hold.
BUFANO'S DREAM The 14-foot-high monument of red granite and stainless steel is by Beniamino Bufano, an Italian-American sculptor and a pacifist and friend of Henry Miller and Ansel Adams.
The 344-foot-high monument was built by Pharaoh Sneferu about 4,600 years ago and is known to contain at least two chambers.
