The US Military Academy cadet, set to graduate in 2021, is "being reported as unaccounted for" while military, federal, state and local law enforcement agencies conduct a search, the academy said in a statement.
The academy does not believe the cadet is carrying any ammunition, nor does it believe he "poses a threat to the public", but "he may be a danger to himself".
Military police patrols have increased across campus and at sporting events.
The cadet was last seen on campus at 5.30pm on 18 October and he failed to report to that weekend's military skills competition as scheduled. Following an initial search, military police descended on the academy at 1am on Sunday and continued searching throughout the day.
The academy has notified New York State Police, Orange County Sheriff's Department and area hospitals and emergency rooms. The US Coast Guard began searching shorelines and state police performed helicopter, drone and K9 sweeps on Sunday.
Academy Superintendent Lt Gen Darryl Williams said search efforts will continue "with all means possible, on and off West Point".
The four-year university, among five US service academies, was founded in 1802 and counts US presidents and other prominent officials among its alumni. It accepts roughly 1,300 students each year.
In June, a five-ton truck overturned and killed a West Point cadet and injured 21 others on the way to a military exercise fewer than eight miles from campus. The soldier behind the wheel faces charges including involuntary manslaughter, negligent homicide, reckless driving and dereliction of duty.
The cadet who was killed died at the scene of the accident, which also injured two trainers and 19 cadets.