The authorities say they believe a disgruntled missing soldier was behind the killings.
A government statement said the deaths were not an attempted coup or connected to the drugs trade.
The victims included eight soldiers and three civilians, two of them Spanish nationals.
The Spaniards were working on repairs at a hilltop communications hub protected by soldiers at the barracks.
A police officer found the bodies at about midday local time (13:00 GMT) at the Monte Tchota barracks north of the capital Praia on the biggest island, Santiago, Cape Verde Television said.
It said police later found an abandoned car containing eight Kalashnikovs and ammunition.
The former Portuguese colony, an archipelago about 600km (370 miles) off the coast of Senegal with a population of 500,000 people, has been praised by international organisations for its commitment to democracy and development.
However, it has also been targeted by international drug rings as a destination for smuggling cocaine.
Last week police seized 280kg of cocaine from a yacht and officials have linked two recent attacks on public figures to the drugs trade.
A new government took office last Friday following an election in March and has promised a zero tolerance approach to crime.
Police in the Cape Verde islands off north-west Africa say they have found the bodies of 11 people, including eight soldiers, at a military barracks.