Authorities said the three Indonesians went missing on Wednesday in waters bordering the Philippines and Malaysia but the circumstances of their disappearance were still unknown.
"They are missing but we don't have confirmation yet on who took them and where they were taken," regional military commander Major General Carlito Galvez told AFP.
"Because of that, we do not consider them kidnap victims yet."
Malaysia's Bernama news agency reported that the missing Indonesians' boat had been found crewless with its engine running.
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The spike in abductions sparked Indonesian warnings that the region could become the "next Somalia" and pushed the three neighbours to pledge coordinated patrols.
The International Maritime Bureau said this month the number of maritime kidnappings hit a 10-year high in 2016, with waters off the southern Philippines becoming increasingly dangerous.
Abu Sayyaf are based on remote and mountainous southern Philippine islands. Their leaders pledge allegiance to the Islamic State group, but analysts say they are more focused on lucrative kidnappings.