The incident occurred December 14 when Spain's airport authority received a call with a recorded voice threatening a flight bound for Sao Paulo, Brazil from Barajas using phrases including "today people will die" in Spanish,the statement said. On board were 315 passengers and 16 crew.
The plane was escorted back to the airport by Spanish air force fighters.
A runway was closed as passengers and cargo were inspected, but police found no explosives and the incident was declared a false alarm.
The passenger had been refused entry into Schengen territory because of a prohibition order issued by Switzerland, the statement said.
The suspects were in custody today in a jail in the city of Tarrancon, midway between Madrid and Cuenca, pending an appearance before an investigating magistrate, the statement said.
Authorities might seek to recover the cost of the airport security operation that exceeded 200,000 euros (USD 228,000), the statement said.