ABS-CBN quoted Lieutenant Colonel Ronaldo Mateo of the 11th Infantry Division of the Philippine army as saying that the first explosion occurred at 12 noon on August 24 in front of a food store on Serantes Street in Jolo Town.
The target appears to be a military truck parked in front of a commercial building near the town square, according to The Straits Times.
In an official report, the Jolo police said a motorbike parked near the M35 of the 21st Infantry Battalion exploded, causing "many casualties".
An hour later, a second explosion occurred on the other side of the road, about 70 meters from the first, in front of a bank.
Lieutenant Colonel Mateo said the double blast killed five soldiers, injured 18 of their comrades and about 20 civilians.
Jolo police confirmed the deaths of four civilians.
The military spokesman, Major General Edgard Arevalo, said the soldiers were "dissolving and treating the casualties while maintaining regional security."
The 11th Infantry Division and the Sulu Provincial Special Forces are in a state of high vigilance after the incident, Arevalo said.