The crew were travelling on two boats that were transporting coal from Borneo island to the Philippines when they were hijacked, said Indonesian Foreign Minister Retno Marsudi.
It is not clear when the vessels -- a tugboat and a barge -- were hijacked but the boats' owners received a ransom call from someone claiming to be from the Abu Sayyaf militant group on Saturday, she said.
The Philippine military said they had heard reports the sailors may have been taken by an Abu Sayyaf faction to one of their hideouts in the conflict-wracked south, but were still working to get confirmation.
Their most recent high-profile kidnapping was of two Canadians and a Norwegian from yachts at a marina in September, with the militants setting an April deadline for millions of dollars in ransom money to be paid.
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In the latest case, Marsudi said the hijackers had contacted the boats' owners twice since Saturday and had sought a ransom, but refused to say how much was demanded.
"Our priority is the safety of the 10 Indonesians who are being held hostage, we will keep working hard to save them," the minister told reporters, adding she had been in touch with her Philippine counterpart.
Major General Demy Tejares, deputy commander of a task force overseeing southern islands in the Philippines, said authorities were working to confirm the kidnapping had occurred.
He said initial information from sources on the ground indicated the sailors may have been taken by an Abu Sayyaf faction to Sulu, a remote island in the country's southwestern tip that is a hideout of the militant outfit.