Judicial police commander Luis Ramirez says the man was arrested Wednesday on the outskirts of Colombia's capital, Bogota. The suspect's name was not officially released.
The man is accused of posting a message reading, "I promise to kill Jeronimo Alberto Uribe, son of Alvaro Uribe," on the social networking site Facebook in July.
The prosecutor's office says the man also had threatened the president on an undisclosed social network.
Police said he will be charged with instigating criminal activity.