The operation is being seen as a major victory for the Philippine military and a huge blow for Abu Sayyaf.
The group had, over the past year, enjoyed a resurgence of activity as it attempted to regain its former strength.
Last year, the Abu Sayyaf wing led by Parad held three employees of the International Committee of the Red Cross hostage captive for several months on Jolo.
Earlier on Sunday, a high-ranking Philippine military commander said at least six al-Qaeda-linked fighters had been killed by soldiers in the assault on an Abu Sayyaf base in Jolo.
Lieutenant-Geneneral Benjamin Dolorfino, head of the military's Western Mindanao Command, said a marine special operations platoon raided the camp following intelligence reports that two wanted fighters were there.
He said the body of Parad was identified by civilians who personally knew him.
The operation was based on a "very strong intelligence report" that the two commanders - Umbra Jumdail in addition to Albader Parad - were in the camp, Dolorfino said.
Lieutenant-Colonel Edgard Arevalo, the Philippine marines' spokesman, said one marine was killed and three others were wounded in the fighting.
The recovery of the dead fighters and their weapons indicated the Abu Sayyaf men were caught by surprise and could have suffered more casualties since it was unusual for them to leave the bodies of dead comrades behind, the Philippine military said.
It said the 30-man marine platoon was backed by other troops deployed to block the escape of the fighters from their encampment on Jolo, where Abu Sayyaf has operated for years despite a US-backed military campaign against them.
Sunday's clash came just three days after Philippine authorities arrested another Abu Sayyaf member who had been on the run for nine years.
Jumadail Arad was allegedly on a mission to buy firearms for the group when he was arrested on Thursday in a joint navy and police intelligence operation.
The Abu Sayyaf is a self-styled group of Muslim fighters blamed for the Philippines's worst attacks, including the bombing of a passenger ferry on Manila Bay that killed over 100 people in 2004.
Abu Sayyaf, which has about 400 fighters, has been blamed for numerous bombings, beheadings and kidnappings of Filipinos and foreigners, including Americans.
Several Filipinos have been kidnapped but most either escaped or were released, allegedly after ransom payments.
Abu Sayyah is believed to have received funds from al-Qaeda and is on a US list of "terrorist" organisations.