The government said in a statement that two Spanish technicians and a local civilian were among those killed yesterday in Monte Tchota, north of the capital Praia, at the army-guarded centre.
"Eleven people have lost their lives," the statement said. "The victims were all male, aged between 20 and 51."
It added: "A soldier who worked in the military centre has been reported missing and there are strong indications that he carried out this attack."
"The airports are functioning normally," it said.
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It also added that there was "no link between these events and drug-trafficking", following media reports that raised the possibility of an attack in retaliation for recent major drug seizures on the archipelago.
"According to preliminary information, the motivations for these events were personal, which excludes the theory of an attack against the state of Cape Verde," the government said.
"The authorities are taking all necessary measures to shed light on this affair", it added, deploring the shooting as a "tragedy".
Spain's foreign ministry confirmed the deaths of two Spanish citizens.
Cape Verde, an impoverished archipelago lying 500 kilometres (300 miles) off the coast of Senegal, is a former Portuguese colony that is home to half a million people.