The three suspects, who are legal residents of Spain, were arrested in two neighbourhoods of Madrid in the early hours, authorities said in a statement.
Interior Minister Jorge Fernandez Diaz said that, unlike in other cases of suspected jihadists arrested in recent months in the country, the suspects were "not devoted to attracting, indoctrinating, radicalizing, or recruiting" people to travel to Syria or Iraq to join Isis.
"Their goal was to act in Spain," he said on Cadena Ser radio.
Europe has been grappling with a growing number of jihadist cells on its territory and radicalized Muslims leaving to fight for Isis or joining the rebels in Iraq and Syria.
More than 100 people from Spain are suspected of having joined jihadist fighters in Iraq and Syria and authorities fear they may return to launch attacks.
Spain has arrested several dozen suspected IS recruiters in recent months.
Some 171 suspected jihadists have been detained in security operations since December 2011, according to the interior minister.