The casualties were among 14 prisoners who escaped from a police station jail in war-torn Jolo, authorities said.
Jolo is a base of the Abu Sayyaf kidnap-for-ransom group and some of the inmates were linked to the militants, according to provincial police chief Senior Superintendent Mario Buyuccan.
"They cut the bars of the jail and jumped from the second floor to the roof of the municipal hall building next door. Our troops responded and the inmates were killed and wounded in hot pursuit operations," Buyuccan told AFP.
"Some inmates are associated with the membership of the Abu Sayyaf."
The injured inmate was recaptured while soldiers and policemen were chasing the remaining 10 escapees. The jail had a total of 32 inmates mostly facing drug charges, Buyuccan added.
The Philippines frequently has mass escapes from prisons which are usually overcrowded, poorly maintained and inadequately guarded.
In the country's biggest jailbreak, more than 150 inmates ecaped a prison in the southern Philippines in January after about a hundred gunmen stormed the facility.
In May, Islamist militants waving black flags of the Islamic State group went on a rampage in the southern city of Marawi and freed 100 inmates from two jails there.
The incident triggered an ongoing US-backed military offensive involving air strikes and artillery barrages to flush out the militants.
Buyuccan said there was no connection between Sunday's jailbreak and the fighting in Marawi, which had killed more than 500 people.