"Five are Spanish nationals of Syrian, Jordanian and Moroccan origin, and two are Syrian and Moroccan nationals," it said.
The arrests were made in the context of an investigation launched in 2014 into "foreign structures" providing logistical support for Islamic State - also called ISIL, ISIS or Daesh - and the Al-Nusra Front, an Al-Qaeda affiliate in Syria, police said.
One of those arrested was a man who dispatched "military material, money, electronic and transmission material, firearms and precursors for making explosives" to Syria and Iraq via a company, it said.
This was shipped out in closed containers under the guise of humanitarian aid, and financed by "hawala," an informal system of payment based on trust that is far more difficult to trace than bank transfers. The leader of the network was in "constant" contact with a member of the Islamic State, who repeatedly asked him to recruit women in order to marry them off to IS jihadists in Syria, the statement said.