Two of the suspects had been practicing flying light aircraft, according to Spanish authorities.
A Russian, a Turk and a Russian of Chechen descent were arrested. Two of the suspects were detained near Ciudad Real traveling toward the northern Spanish border with France. One suspect was arrested in the southern city of La Linea, bordering Gibraltar.
Explosives were found in the La Linea house where one of the suspects lived. There were enough explosives to blow up a bus, according to Spanish police.
"This is one of the most important operations carried out against al Qaeda," said Spain's Interior Minister Fernandez Diaz. He said the operation involved close collaboration with intelligence services from "Spain's allies," without identifying any of the countries.
The arrests came as the Summer Olympics were being held in Britain under tight security against possible terrorist attacks, including military aircraft and ground-to-air missiles.
Spanish authorities had been watching the suspects for "some time," the minister said and decided to arrest them after the two Russians took a bus toward France.
The minister described one operative as a key member of the terror network, and said both of the Russians had practiced flying in light aircraft, without saying where or whether authorities suspect they might have been plotting an attack using aircraft. One of the Russians was also an expert in explosives and poisonous substances, said Fernandez Diaz.
Spanish police have arrested dozens of al Qaeda suspects since the Sept. 11, 2001, attacks in the United States and the 2004 train bombings in Madrid.
"What jumps out is that they have had aircraft training," he said. "It's always a worry that someone could get a hold of a private plane and try to do a (terror) operation against an event," Ranstorp said.
But getting to Britain during the Olympics probably would have been a challenge for the three, even if they had not been under surveillance.
Passport-free ground travel in much of the 27-nation European Union meant they could have gone to countries on the continent without facing document checks, but getting to Britain is more difficult because passport checks for visitors are mandatory.
The three will appear soon before an investigating magistrate at the National Court in Madrid and remain under detention while a judge studies the case and decides on possible charges. That process could take anywhere from days to months, and authorities are not likely to release more details about the case until the judge finishes that work.
The Associated Press contributed to this report.