JSU campus authorities say in a news release that Jhamerius Mack was arrested March 5 and charged with two counts of felony cyberstalking.
The university says Mack is not a student at the school.
Mack is jailed at the Hinds County Detention Center in Raymond under a $10,000 bond.
JSU spokesman Eric Stringfellow says threats were made against Meyers, named JSU's first female chief in December of 2010. Stringfellow says the threats of bodily harm to Meyers were posted on Facebook in February.
No other details were released.
Cyberstalking is punishable in Mississippi by up to five years in jail, up to a $10,000 fine or both.