The trawler was intercepted by two navy ships on Friday after receiving information that a ship wanted by Interpol in Argentina had been spotted in Aceh, in the northwest of Sumatra, navy spokesman Edi Sucipto told AFP.
The boat has been taken to a naval base in Belawan, North Sumatra for investigation.
"We are currently questioning the crew to find out more about the case," Sucipto said, adding that one of them had a gunshot wound to his leg.
The Chinese trawler was previously reported to have been fishing illegally in Argentine waters in late February.
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Argentine forces in March opened fire on and a sank a Chinese boat illegally fishing in the South Atlantic after it attempted to ram a coast guard vessel.
Indonesia in 2014 launched a tough crackdown on illegal fishing which involves sinking foreign vessels caught fishing without a permit after impounding the boats and removing the crews.
Its foreign minister protested to Beijing after the Chinese coastguard last month stopped an Indonesian patrol boat from detaining a Chinese trawler.