The vessel was conducting a torpedo drill on Wednesday but failed to relay the results as expected, a navy spokesman said.
A search is under way for the German-made submarine, KRI Nanggala-402, and its crew.
Indonesia has asked authorities in Australia and Singapore for help with the hunt, the country's military chief Hadi Tjahjanto told Reuters.
"We are still searching in the waters of Bali, 60 miles (96km) from Bali, (for) 53 people," he told the news agency in a text message.
He added that contact with the submarine was lost at around 4.30am local time, and that the navy has deployed warships to search the area.
The 1,395-tonne vessel was built in 1978, according to the Indonesian cabinet secretariat's website.