Prosecutors said in a statement that the Colombian citizen made the threats online and they were written in Arabic.
The concert in the city of Alajuela went ahead as scheduled.
The threat comes almost two months after a 22-year-old man detonated a homemade bomb at the exit of the Manchester Arena in Manchester, England, shortly after a Grande concert. 23 people, including the attacker, were killed with 250 people injured.
The singer put together a benefit concert, titled "One Love Manchester," on June 4, which featured performances by Justin Bieber, Miley Cyrus, Pharrell, Niall Horan, Coldplay and Katy Perry. All the benefits went to the victims and their families.
The "Dangerous Woman" singer posted a statement following the attack, in which she said, "We won't let hate win."
Representatives for Grande have not yet responded to TheWrap's request for comment.