Airport Aviation Director Frank Miller said all flight operations were canceled for the afternoon and people were being encouraged to stay away from the airport, the San Antonio Express-News reported.
A police spokeswoman said a man with "an accent" called the airport about 2:15 p.m. and said "he had left luggage at the airport and the airport was going to blow up," the newspaper said.
Police Chief William McManus said the caller also said there were explosives in three cars parked in the lower level of the airport's short-term parking garage, the newspaper said. Two of the cars had been cleared without any explosives being found and a bomb squad was checking the third vehicle.
The threat prompted authorities to get about 1,000 people out of the terminals while the bomb squad and other law enforcement units checked out the airport. People were allowed back into the terminals within about 2 hours, airport officials said.
Aircraft that landed before the threat were held on the tarmac with their passengers still aboard.