The teenager was arrested from his home in Sandwell this morning on suspicion of malicious communications.
West Midlands Police say the social media post caused "a considerable amount of fear and distress" for pupils at the school.
A spokesperson for the force said: "We are working with the school to reassure staff and pupils that action has been taken swiftly.
"We do take threats of this nature incredibly seriously and we will have officers at the school as it closes today for half term to respond to any ongoing concerns."
#ARREST |— Wednesbury Town Police (@WednesburyWMP) May 26, 2023
We’ve arrested a 16-year-old schoolboy from his home address in #Sandwell this morning on suspicion of malicious communications after we were alerted to an alarming social media post. pic.twitter.com/52qIWsCwbW