The 21 from countries including Bangladesh, India and Pakistan were found floating off Jayanti Beach, Cianjur, early on Wednesday, local website Okezone reported.
Reports say they had set out for Christmas Island but were hampered by big waves, and they floated for three days without fuel before local fishermen found them.
"When we found them, they were lacking food and drink," a fisherman named Mamun told Okezone.
"Most of them are adults and some brought kids.
"We took them to the beach and then they were secured in Cidaun Police Station."
Immigration officials were preparing to collect information from the asylum seekers, the report said.
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