Presidential spokesman Willy Nyamitwe said Saturday that Col. Jean Bikomagu was shot in his car.
Burundi has been rocked by violence since the April announcement that Nkurunziza would stand for another term.
Nkurunziza won the elections following turmoil in which about 100 people died in months of street protests against the extension of the president's time in power.
Recently officials from both the government and opposition have been targeted. Earlier this month Gen. Adolphe Nshimirimana, the president's senior adviser on security matters, was killed when a rocket was fired at his car.