The threat comes after suicide bomber Salman Abedi detonated a home-made device at the US pop star’s show at Manchester Arena in May, killing 22 people including seven children.
Costa Rican prosecutors said in a statement that the suspect was a Colombian man of 22, who made the threats online.
The concert in the city of Alajuela, Costa Rica, went ahead as scheduled on Sunday. Fans had to pass through three security checks for Sunday’s gig.
Head investigator Walter Espinoza told local media that the threats were written in Arabic.
He identified the suspect only by the last names Caicedo Lopez.