Two of those arrested were intercepted early Thursday in Almuradiel, traveling by bus from Cadiz to Irun and ultimately to France, El Diario reported.
They were described as citizens "of Eurasian republics of the former USSR" and "extremely dangerous people" by Interior Minister Jorge Fernandez.
The third person, a Turkish man was found in an apartment the three rented in Cadiz where police also found enough explosive materials to "destroy an entire bus," Fernandez said.
"There are clear indications that they could plan an attack in Spain and/or another European country," Fernandez said.
What led to the arrests was not reported, but Fernandez said it was made possible with the help of law enforcement agencies of other countries.