"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.
The West African nation 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 Joao Bernardo "Nino" Vieira, a former ruler, 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.