Sunday's events underscored the chronic instability of the former Portuguese colony.
In November, renegade soldiers attacked the home of Joao Bernardo Vieira, the president, with automatic weapons, killing at least one guard in a failed coup attempt that was repulsed by loyalist security forces.
Na Waie's killing has once again thrown the west African nation into chaos, just months after after it held a general election.
Nhamtchio told the AFP news agency that Waie was "gravely wounded and did not survive his injuries", adding that five others were also hurt in the blast.
One of the general's bodyguards, speaking anonymously to the AFP, said the bomb was placed under the stairway leading to Na Waie's office and the blast triggered the collapse of a large section of the main headquarters building, where the general's office was located.
"He had just reached the first steps when the bomb was triggered. He was mortally injured," the bodyguard said.
Government troops closed down roads around the army building and shut down five private radio stations after the attack.
Guinea-Bissau has lurched from one political crisis to another since independence from Portugal in 1974 and Na Waie's predecessor, General Verissimo Correia Seabra, was shot dead by soldiers in October 2004.
Na Wai served in the military government that overthrew Vieira in the 1990s and had been critical of him since Vieira was voted back to the presidency in 2005.
Analysts say instability has been worsened by the presence of international drug trafficking organisations which use the country as a staging post for smuggling cocaine into Europe.