Huge columns of smoke rose from the area of the military complex in the capital's center on the second day of the Muslim feast of Eid al-Adha, despite separate unilateral truces announced by the warring generals for the holiday.
Deadly fighting since mid-April between forces loyal to army chief Abdel Fattah al-Burhan and the paramilitary Rapid Support Forces (RSF) has left millions of Khartoum residents trapped, rationing electricity and water in the oppressive heat.
Residents seven kilometers away from the army headquarters "felt the tremor in their walls," one of them told AFP.
The source of the explosion could not be immediately verified, and there was no immediate word on casualties.
In northwest Khartoum, army fighter jets launched "air strikes on RSF troops," witnesses said.
The brutal war has killed at least 2,800 people, according to the Armed Conflict Location and Event Data Project.
The tally is a conservative estimate, with many of the injured unable to reach health facilities and bodies left in the streets in both Khartoum and the western region of Darfur, where most of the violence has occurred.
The war has sent 645,000 people fleeing across borders, according to the United Nations, with around 2.2 million more displaced within the country.
The fighting, which erupted on April 15, has shown no signs of abating as experts say both sides refuse to negotiate before claiming military advantage.
Burhan this week called for Sudanese "youth and all those able to defend" to take up arms with the military to defend against the "existential threat" posed by the RSF.
The call has been widely rejected by civilians, themselves raising alarms that what began as a power struggle between generals is spiralling into civil conflict.
The U.N. has warned that attacks by the RSF and allied ethnically Arab militias in Darfur could constitute "crimes against humanity."