Detectives launched a manhunt on Saturday after threatening messages were posted in Arabic on a webpage of the concert organisers.
The suspect, with the last names Caicedo Lopez, a 22-year-old from Colombia, was held in a 6am raid on his flat in Tibas, near the capital San Jose, yesterday.
Officers seized two mobile phones allegedly used to make the threats.
On May 22 a suicide bomber killed 22 people and injured 119 more at a concert by the American singer in Manchester, and Costa Rican police feared a copycat attack was being planned.
The manhunt was lead by the Judicial Investigation Department (OIJ) and the raid was carried out by its Special Tactical Response Unit.
The director of the OIJ, Walter Espinoza, said: 'The original threat was in the Arabic language and indicated that there could be a situation of danger or an attack at the concert. It was a very sensitive situation.'
Police launched the dawn raid after tracing the threats to the suspect's home. The investigation was carried out jointly with the Department of Intelligence and National Security and the Ministry of Public Security.
Caicedo Lopez was described as having no police record in Costa Rica. After being arrested he was handed over to state prosecutors.
Ariana Grande, 23, later performed for 14,000 fans as planned at the Parque Viva.
The singer, 23, later performed for 14,000 fans as planned at the Parque Viva music venue (pictured)
Organisers said in a statement: 'The operation was carried out with total professionalism.'
On Saturday police carried out an emergency drill to check security arrangements at the park ahead of the concert.
All fans were searched as they passed through three rings of security.