Princeton Police Chief James Waters said a juvenile suspect who does not attend the school posted the threats on an app called Burn Book.
Police and school officials identified him using a picture he also posted on the app. He was then taken into custody and his home was searched, Waters said.
The school district alerted parents overnight using email and social media.
Officers were on all the school campuses in Princeton throughout the day Wednesday to ensure student safety.
Students at Princeton High School also had to pass through metal detectors when they arrived for classes in the morning.
The unnamed suspect is expected to be charged with making a terroristic threat, which is a Class B misdemeanor.