Luis Sanca, security adviser to Prime Minister Carlos Gomes Jr., confirmed the president had died but gave no details.
The military said the armed forces would respect the constitutional order, which calls for parliament chief Raimundo Pereira to succeed the president in the event of his death.
It also dismissed claims that the armed forces headquarters was implicated in Vieira's killing as a retaliation for the assassination late Sunday of armed forces chief of staff Gen. Batiste Tagme na Waie at his headquarters in Bissau.
The two men were considered staunch political rivals and both had survived assassination attempts in recent months.
The former Portuguese colony has suffered multiple coups and attempted coups since 1980, when Vieira himself first took power in one. The United Nations says Guinea-Bissau, an impoverished nation on the Atlantic coast of Africa, has become a key transit point for cocaine smuggled from Latin America to Europe.
Bissau was remarkably calm on Monday despite the president's death, and traffic flowed normally in some parts of town.
Just hours after Waie's death late Sunday, volleys of automatic gunfire were heard for at least two hours before dawn in Bissau and residents said soldiers had converged on Vieira's palace.
The Portuguese news agency LUSA reported that troops attacked with rockets and rifles. The president's press chief, Barnabe Gomes, escaped from the house after being struck by a bullet in his right shoulder, LUSA said.
It was the second attack on Vieira in recent months. In November, Vieira's residence was attacked by renegade soldiers with automatic weapons. At least one guard was killed in the failed coup attempt that was repulsed by loyalist security forces.
Waie also survived an apparent assassination attempt when unidentified attackers opened fire on his car in January.
It was not immediately clear what caused the blast that killed Waie. Defense Minister Artur Silva and other top officials contacted by The Associated Press declined to comment.